From 7e0f330c5451ceb426bcc0f0418e79b4adada582 Mon Sep 17 00:00:00 2001 From: Manas Rachh Date: Tue, 25 Jul 2023 10:13:37 -0400 Subject: [PATCH 01/23] adding docs makefile and updating theme --- docs/Makefile | 216 ++++++++++++++++++++++++++++++++++++++++++ docs/_static/.keep | 0 docs/_templates/.keep | 0 docs/conf.py | 2 +- 4 files changed, 217 insertions(+), 1 deletion(-) create mode 100644 docs/Makefile create mode 100644 docs/_static/.keep create mode 100644 docs/_templates/.keep diff --git a/docs/Makefile b/docs/Makefile new file mode 100644 index 0000000..bfded92 --- /dev/null +++ b/docs/Makefile @@ -0,0 +1,216 @@ +# Makefile for Sphinx documentation +# + +# You can set these variables from the command line. +SPHINXOPTS = +SPHINXBUILD = sphinx-build +PAPER = +BUILDDIR = _build + +# User-friendly check for sphinx-build +ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1) +$(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/) +endif + +# Internal variables. +PAPEROPT_a4 = -D latex_paper_size=a4 +PAPEROPT_letter = -D latex_paper_size=letter +ALLSPHINXOPTS = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . +# the i18n builder cannot share the environment and doctrees with the others +I18NSPHINXOPTS = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . + +.PHONY: help +help: + @echo "Please use \`make ' where is one of" + @echo " html to make standalone HTML files" + @echo " dirhtml to make HTML files named index.html in directories" + @echo " singlehtml to make a single large HTML file" + @echo " pickle to make pickle files" + @echo " json to make JSON files" + @echo " htmlhelp to make HTML files and a HTML help project" + @echo " qthelp to make HTML files and a qthelp project" + @echo " applehelp to make an Apple Help Book" + @echo " devhelp to make HTML files and a Devhelp project" + @echo " epub to make an epub" + @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter" + @echo " latexpdf to make LaTeX files and run them through pdflatex" + @echo " latexpdfja to make LaTeX files and run them through platex/dvipdfmx" + @echo " text to make text files" + @echo " man to make manual pages" + @echo " texinfo to make Texinfo files" + @echo " info to make Texinfo files and run them through makeinfo" + @echo " gettext to make PO message catalogs" + @echo " changes to make an overview of all changed/added/deprecated items" + @echo " xml to make Docutils-native XML files" + @echo " pseudoxml to make pseudoxml-XML files for display purposes" + @echo " linkcheck to check all external links for integrity" + @echo " doctest to run all doctests embedded in the documentation (if enabled)" + @echo " coverage to run coverage check of the documentation (if enabled)" + +.PHONY: clean +clean: + rm -rf $(BUILDDIR)/* + +.PHONY: html +html: + $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html + @echo + @echo "Build finished. The HTML pages are in $(BUILDDIR)/html." + +.PHONY: dirhtml +dirhtml: + $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml + @echo + @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml." + +.PHONY: singlehtml +singlehtml: + $(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml + @echo + @echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml." + +.PHONY: pickle +pickle: + $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle + @echo + @echo "Build finished; now you can process the pickle files." + +.PHONY: json +json: + $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json + @echo + @echo "Build finished; now you can process the JSON files." + +.PHONY: htmlhelp +htmlhelp: + $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp + @echo + @echo "Build finished; now you can run HTML Help Workshop with the" \ + ".hhp project file in $(BUILDDIR)/htmlhelp." + +.PHONY: qthelp +qthelp: + $(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp + @echo + @echo "Build finished; now you can run "qcollectiongenerator" with the" \ + ".qhcp project file in $(BUILDDIR)/qthelp, like this:" + @echo "# qcollectiongenerator $(BUILDDIR)/qthelp/finufft.qhcp" + @echo "To view the help file:" + @echo "# assistant -collectionFile $(BUILDDIR)/qthelp/finufft.qhc" + +.PHONY: applehelp +applehelp: + $(SPHINXBUILD) -b applehelp $(ALLSPHINXOPTS) $(BUILDDIR)/applehelp + @echo + @echo "Build finished. The help book is in $(BUILDDIR)/applehelp." + @echo "N.B. You won't be able to view it unless you put it in" \ + "~/Library/Documentation/Help or install it in your application" \ + "bundle." + +.PHONY: devhelp +devhelp: + $(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp + @echo + @echo "Build finished." + @echo "To view the help file:" + @echo "# mkdir -p $$HOME/.local/share/devhelp/finufft" + @echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/finufft" + @echo "# devhelp" + +.PHONY: epub +epub: + $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub + @echo + @echo "Build finished. The epub file is in $(BUILDDIR)/epub." + +.PHONY: latex +latex: + $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex + @echo + @echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex." + @echo "Run \`make' in that directory to run these through (pdf)latex" \ + "(use \`make latexpdf' here to do that automatically)." + +.PHONY: latexpdf +latexpdf: + $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex + @echo "Running LaTeX files through pdflatex..." + $(MAKE) -C $(BUILDDIR)/latex all-pdf + @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex." + +.PHONY: latexpdfja +latexpdfja: + $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex + @echo "Running LaTeX files through platex and dvipdfmx..." + $(MAKE) -C $(BUILDDIR)/latex all-pdf-ja + @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex." + +.PHONY: text +text: + $(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text + @echo + @echo "Build finished. The text files are in $(BUILDDIR)/text." + +.PHONY: man +man: + $(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man + @echo + @echo "Build finished. The manual pages are in $(BUILDDIR)/man." + +.PHONY: texinfo +texinfo: + $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo + @echo + @echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo." + @echo "Run \`make' in that directory to run these through makeinfo" \ + "(use \`make info' here to do that automatically)." + +.PHONY: info +info: + $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo + @echo "Running Texinfo files through makeinfo..." + make -C $(BUILDDIR)/texinfo info + @echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo." + +.PHONY: gettext +gettext: + $(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale + @echo + @echo "Build finished. The message catalogs are in $(BUILDDIR)/locale." + +.PHONY: changes +changes: + $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes + @echo + @echo "The overview file is in $(BUILDDIR)/changes." + +.PHONY: linkcheck +linkcheck: + $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck + @echo + @echo "Link check complete; look for any errors in the above output " \ + "or in $(BUILDDIR)/linkcheck/output.txt." + +.PHONY: doctest +doctest: + $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest + @echo "Testing of doctests in the sources finished, look at the " \ + "results in $(BUILDDIR)/doctest/output.txt." + +.PHONY: coverage +coverage: + $(SPHINXBUILD) -b coverage $(ALLSPHINXOPTS) $(BUILDDIR)/coverage + @echo "Testing of coverage in the sources finished, look at the " \ + "results in $(BUILDDIR)/coverage/python.txt." + +.PHONY: xml +xml: + $(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml + @echo + @echo "Build finished. The XML files are in $(BUILDDIR)/xml." + +.PHONY: pseudoxml +pseudoxml: + $(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml + @echo + @echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml." diff --git a/docs/_static/.keep b/docs/_static/.keep new file mode 100644 index 0000000..e69de29 diff --git a/docs/_templates/.keep b/docs/_templates/.keep new file mode 100644 index 0000000..e69de29 diff --git a/docs/conf.py b/docs/conf.py index c7eff8a..15d33c1 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -83,7 +83,7 @@ # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # -html_theme = 'alabaster' +html_theme = 'sphinx_rtd_theme' # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the From 0d5e94ae560dcf70906e1c34140e30eb0821629d Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Tue, 25 Jul 2023 10:49:25 -0400 Subject: [PATCH 02/23] small update to config --- docs/conf.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/conf.py b/docs/conf.py index 15d33c1..ff11cad 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -64,7 +64,7 @@ # # This is also used if you do content translation via gettext catalogs. # Usually you set "language" from the command line for these cases. -language = None +language = 'en' # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. From c592e9ad55144afdf6c6bf02caf92101bbb22142 Mon Sep 17 00:00:00 2001 From: jghoskins Date: Tue, 25 Jul 2023 16:17:38 -0500 Subject: [PATCH 03/23] verts2edge renaming --- chunkie/@chunkgraph/chunkgraph.m | 24 +++++++++---------- chunkie/@chunkgraph/findregions.m | 4 ++-- chunkie/@chunkgraph/vertextract.m | 4 ++-- chunkie/chunkgraphinit.m | 18 +++++++------- devtools/test/chunkgrphconstructTest.m | 16 ++++++------- devtools/test/chunkgrphrcipTest.m | 16 ++++++------- devtools/test/chunkgrphrcipTransmissionTest.m | 8 +++---- devtools/test/chunkrgrphOpdimTest.m | 6 ++--- 8 files changed, 48 insertions(+), 48 deletions(-) diff --git a/chunkie/@chunkgraph/chunkgraph.m b/chunkie/@chunkgraph/chunkgraph.m index cf7c4f9..ac85649 100644 --- a/chunkie/@chunkgraph/chunkgraph.m +++ b/chunkie/@chunkgraph/chunkgraph.m @@ -8,7 +8,7 @@ % properties(SetAccess=public) verts - edge2verts + verts2edge echnks regions vstruc @@ -25,7 +25,7 @@ end methods - function obj = chunkgraph(verts,edge2verts,fchnks,cparams) + function obj = chunkgraph(verts,verts2edge,fchnks,cparams) if (nargin == 0) return end @@ -33,7 +33,7 @@ return end obj.verts = verts; - obj.edge2verts = edge2verts; + obj.verts2edge = verts2edge; obj.echnks = chunker.empty; if (nargin < 4) @@ -66,15 +66,15 @@ pref.nchmax = 10000; pref.k = 16; - if (size(verts,2) ~= size(edge2verts,2)) + if (size(verts,2) ~= size(verts2edge,2)) error('Incompatible vertex and edge sizes'); end echnks = chunker.empty(); - for i=1:size(edge2verts,1) + for i=1:size(verts2edge,1) if (numel(fchnks) Date: Tue, 25 Jul 2023 23:49:41 -0400 Subject: [PATCH 04/23] add more structure to documentation, mostly a wish list for now --- docs/assets/images/scatter_star_trim.png | Bin 0 -> 285231 bytes docs/conf.py | 4 +- docs/gallery.rst | 6 ++ docs/getchunkie.rst | 18 ++++ docs/guide.rst | 17 ++++ docs/guide/chunkers.rst | 5 + docs/guide/chunkgraphbvps.rst | 25 +++++ docs/guide/chunkgraphs.rst | 3 + docs/guide/largerproblems.rst | 3 + docs/guide/simplebvps.rst | 21 ++++ docs/guide/transmission.rst | 3 + docs/index.rst | 123 ++++++++++++++++++----- 12 files changed, 202 insertions(+), 26 deletions(-) create mode 100644 docs/assets/images/scatter_star_trim.png create mode 100644 docs/gallery.rst create mode 100644 docs/getchunkie.rst create mode 100644 docs/guide.rst create mode 100644 docs/guide/chunkers.rst create mode 100644 docs/guide/chunkgraphbvps.rst create mode 100644 docs/guide/chunkgraphs.rst create mode 100644 docs/guide/largerproblems.rst create mode 100644 docs/guide/simplebvps.rst create mode 100644 docs/guide/transmission.rst diff --git a/docs/assets/images/scatter_star_trim.png b/docs/assets/images/scatter_star_trim.png new file mode 100644 index 0000000000000000000000000000000000000000..a53f65139269bed554d6ec90b1ac3def765e1caf GIT binary patch literal 285231 zcmV)}KzqN5P)004R>004l5008;`004mK004C`008P>0026e000+ooVrmw00006 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b/docs/guide.rst new file mode 100644 index 0000000..6e89f77 --- /dev/null +++ b/docs/guide.rst @@ -0,0 +1,17 @@ +Chunkie User Guide +=================== + + + +.. toctree:: + :maxdepth: 1 + :caption: Contents: + + guide/chunkers + guide/simplebvps + guide/largerproblems + guide/chunkgraphs + guide/chunkgraphbvps + guide/transmission + + diff --git a/docs/guide/chunkers.rst b/docs/guide/chunkers.rst new file mode 100644 index 0000000..2ab865c --- /dev/null +++ b/docs/guide/chunkers.rst @@ -0,0 +1,5 @@ + +Curve Discretization with Chunkers +=================================== + + diff --git a/docs/guide/chunkgraphbvps.rst b/docs/guide/chunkgraphbvps.rst new file mode 100644 index 0000000..a61a095 --- /dev/null +++ b/docs/guide/chunkgraphbvps.rst @@ -0,0 +1,25 @@ + +Boundary Value Problems on Chunkgraphs +========================================= + + +A Sound Hard Scattering Problem with Corners +--------------------------------------------- + + + +An Open Arc Problem +--------------------- + + + +Mixed Boundary Conditions +-------------------------- + + + + + + + + diff --git a/docs/guide/chunkgraphs.rst b/docs/guide/chunkgraphs.rst new file mode 100644 index 0000000..576f4b0 --- /dev/null +++ b/docs/guide/chunkgraphs.rst @@ -0,0 +1,3 @@ + +Describing More Complicated Geometries with Chunkgraphs +======================================================== diff --git a/docs/guide/largerproblems.rst b/docs/guide/largerproblems.rst new file mode 100644 index 0000000..f706bc1 --- /dev/null +++ b/docs/guide/largerproblems.rst @@ -0,0 +1,3 @@ + +Larger Boundary Value Problems +================================ diff --git a/docs/guide/simplebvps.rst b/docs/guide/simplebvps.rst new file mode 100644 index 0000000..b912ed4 --- /dev/null +++ b/docs/guide/simplebvps.rst @@ -0,0 +1,21 @@ + +Solving Standard Boundary Value Problems +========================================= + + + +A Laplace Problem +------------------ + + + +A Helmholtz Scattering Problem +------------------------------- + + + +A Stokes Flow Problem +---------------------- + + + diff --git a/docs/guide/transmission.rst b/docs/guide/transmission.rst new file mode 100644 index 0000000..aa5169d --- /dev/null +++ b/docs/guide/transmission.rst @@ -0,0 +1,3 @@ + +Application to Transmission Problems with Multiple Junctions +============================================================= diff --git a/docs/index.rst b/docs/index.rst index c1022a6..18339ae 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -5,12 +5,13 @@ chunkie -======== - -.. toctree:: - :maxdepth: 2 - :caption: Contents: +========== +.. image:: assets/images/scatter_star_trim.png + :width: 350 px + :alt: scattering by a smooth star domain + :align: center + chunkie is a MATLAB package for solving partial differential equations in two dimensional domains. The name "chunkie" derives @@ -19,27 +20,95 @@ discretize the domain boundary and the use of an integral equation method to solve the PDE. With chunkie, you can solve the Helmholtz equation on an exterior -domain in a few lines of MATLAB: - - import project - # Get your stuff done - project.do_stuff() +domain in a few lines of MATLAB. The code below defines and solves +a scattering problem, producing the image above: + +.. code:: matlab + + % planewave definitions + + kvec = 20*[1;-1.5]; + zk = norm(kvec); + planewave = @(kvec,r) exp(1i*sum(bsxfun(@times,kvec(:),r(:,:)))).'; + + % discretize domain + + chnkr = chunkerfunc(@(t) starfish(t,narms,amp),struct('maxchunklen',4/zk)); + + % build CFIE and solve + + fkern = kernel('helm','c',zk,[1,-zk*1i]); + sysmat = chunkermat(chnkr,fkern); + sysmat = 0.5*eye(chnkr.k*chnkr.nch) + sysmat; + + rhs = -planewave(kvec(:),chnkr.r(:,:)); + sol = gmres(sysmat,rhs,[],1e-13,100); + + % evaluate at targets + + x1 = linspace(-3,3,400); + [xxtarg,yytarg] = meshgrid(x1,x1); + targets = [xxtarg(:).';yytarg(:).']; + + in = chunkerinterior(chnkr,targets); + out = ~in; + + uscat = chunkerkerneval(chnkr,fkern,sol,targets(:,out)); + + uin = planewave(kvec,targets(:,out)); + utot = uscat(:)+planewave(kvec,targets(:,out)); + + % plot + + maxu = max(abs(utot(:))); + figure() + zztarg = nan(size(xxtarg)); + zztarg(out) = utot; + h=pcolor(xxtarg,yytarg,imag(zztarg)); + set(h,'EdgeColor','none') + hold on + plot(chnkr,'LineWidth',2) + axis equal tight + colormap(redblue) + caxis([-maxu,maxu]) Features -------- -- easy-to-use: includes pre-packaged solvers for Laplace, Helmholtz, - and Stokes equations and convenient tools for visualizing - domains and plotting solutions +- easy-to-use: most chunkie functionality only requires that + you specify two things, the geometry (as a "chunker" object) + and the integral kernel (as a "kernel" object). The distribution + includes pre-defined kernels for the Laplace, Helmholtz, + and Stokes PDEs and convenient tools for visualizing domains + and plotting solutions. +- capable: chunkie uses high order accurate quadrature rules + and fast algorithms to provide accurate solutions with linear + scaling. The chunkie utilities can be used to solve singular + problems on domains with corners and multiple material junctions + with relative ease. - flexible: allows you to define your own integral kernels and - use the quadrature routines in a modular fashion -- fast: works with FLAM (fast linear algebra in MATLAB) - for fast, direct integral equation solves + use the quadrature routines in a modular fashion. -Installation ------------- +How to Get Chunkie +------------------- -chunkie is pure MATLAB. You can download ... +- `Get chunkie `_ (includes installation instructions + and troubleshooting guide) +- `Source Code `_ + + +Using Chunkie +---------------- + +The `chunkie guide `_ +provides an overview of the chunkie approach to PDEs and a detailed +look at chunkie's capabilities. + +Gallery +-------- + +The `gallery `_ has examples of chunkie applications +submitted by users. Contributing ------------ @@ -51,6 +120,7 @@ We welcome your collaboration! First, see the - `Source Code `_ + License ------- @@ -58,9 +128,14 @@ The project is licensed under a modified BSD 3-clause license. -Indices and tables -================== -* :ref:`genindex` -* :ref:`modindex` -* :ref:`search` + +.. toctree:: + :maxdepth: 1 + :caption: Contents + + getchunkie + guide + gallery + + From cafc8fb7248226356e60ba2b5a15c43f9034f754 Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Wed, 26 Jul 2023 11:36:03 -0400 Subject: [PATCH 05/23] small changes --- docs/guide/chunkers.rst | 3 +++ 1 file changed, 3 insertions(+) diff --git a/docs/guide/chunkers.rst b/docs/guide/chunkers.rst index 2ab865c..763d69b 100644 --- a/docs/guide/chunkers.rst +++ b/docs/guide/chunkers.rst @@ -2,4 +2,7 @@ Curve Discretization with Chunkers =================================== +In chunkie, a smooth, regular curve is discretized as a +chunker object. The curve is divided up into "chunks" of +curve, each discretized by scaled Legendre nodes. From 93819f2d2ada227abaa2bce7cfa355ce0cdd15f9 Mon Sep 17 00:00:00 2001 From: jghoskins Date: Wed, 26 Jul 2023 11:07:44 -0500 Subject: [PATCH 06/23] region fixes unstable --- chunkie/@chunkgraph/chunkgraph.m | 52 +++++++ chunkie/mergeregions.m | 65 ++++++++ chunkie/pointinregion.m | 19 +++ chunkie/regioninside.m | 20 +++ devtools/test/chunkgrphregionTest.m | 232 ++++++++++++++++++++++++++++ 5 files changed, 388 insertions(+) create mode 100644 chunkie/mergeregions.m create mode 100644 chunkie/pointinregion.m create mode 100644 chunkie/regioninside.m create mode 100644 devtools/test/chunkgrphregionTest.m diff --git a/chunkie/@chunkgraph/chunkgraph.m b/chunkie/@chunkgraph/chunkgraph.m index ac85649..76c6c8a 100644 --- a/chunkie/@chunkgraph/chunkgraph.m +++ b/chunkie/@chunkgraph/chunkgraph.m @@ -122,6 +122,58 @@ regions{i} = region_comp; end + gmat = zeros(numel(regions)); + + for ii=1:numel(regions) + rgna = regions{ii}; + ilist = []; + for jj=1:numel(regions) + if (ii ~=jj) + rgnb = regions{jj}; + [inc] = regioninside(obj,rgnb,rgna); + if (inc) + ilist = [ilist,jj]; + end + end + gmat(ii,ilist) = 1; + gmat(ilist,ii) = 1; + end + imin = min(ilist); + end + + ccomp_reg = conncomp(graph(gmat)); + [s,inds] = sort(ccomp_reg); + regions = regions(inds); + + for ii = 1:numel(s) + si = s(ii); + for jj=1:(numel(s)-1) + sj = s(jj); + if (si == sj) + rgna = regions{jj}; + rgnb = regions{jj+1}; + [inc] = regioninside(obj,rgna,rgnb); + if (inc) + regions([jj,jj+1])= regions([jj+1,jj]); + end + end + end + end + + + rgns = regions; + rgnout = rgns{1}; + if (numel(rgns)>1) + rgn2 = rgns{2}; + [rgnout] = mergeregions(obj,rgnout,rgn2); + for ii=3:numel(rgns) + rgn2 = rgns{ii}; + [rgnout] = mergeregions(obj,rgnout,rgn2); + end + end + + regions = rgnout; + obj.regions = regions; end function obj = set.verts(obj,val) diff --git a/chunkie/mergeregions.m b/chunkie/mergeregions.m new file mode 100644 index 0000000..c484742 --- /dev/null +++ b/chunkie/mergeregions.m @@ -0,0 +1,65 @@ +function [rgnout] = mergeregions(cgrph,rgn1,rgn2) + + rgnout = {}; + + e2 = rgn2{1}{1}(1); + v2 = find(cgrph.verts2edge(:,abs(e2))==1); + v2 = cgrph.verts(:,v2); + + irgn = 0; + for ii=2:numel(rgn1) + nin = pointinregion(cgrph,rgn1{ii},v2); + disp("first inclusion:") + nin + if (nin > 0 && mod(nin,2)==1) + if (irgn ~= 0) + disp("Warning: an unsupported geometry error has occurred"); + end + irgn = ii; + end + end + + if (irgn ~= 0) + rgnout = rgn1; + rgnout = [rgnout,rgn2(2:end)]; + rgnout{irgn} = [rgnout{irgn},rgn2{1}]; + end + + irgn1 = irgn; + + if (irgn == 0) + e1 = rgn1{1}{1}(1); + v1 = find(cgrph.verts2edge(:,abs(e1))==1); + v1 = cgrph.verts(:,v1); + + irgn = 0; + for ii=2:numel(rgn2) + nin = pointinregion(cgrph,rgn2{ii},v1); + disp("second inclusion:") + nin + if (nin > 0 && mod(nin,2)==1) + if (irgn ~= 0) + disp("Warning: an unsupported geometry error has occurred"); + end + irgn = ii; + end + end + + if (irgn ~= 0) + disp("here") + irgn + rgnout = rgn2; + rgnout = [rgnout,rgn1(2:end)]; + rgnout{irgn} = [rgnout{irgn},rgn1{1}]; + end + end + + if (irgn1==0 && irgn==0) + disp("here also") + rgnout = rgn1; + rgnout = [rgnout,rgn2(2:end)]; + rgnout{1} = [rgnout{1},rgn2{1}]; + end + +end + diff --git a/chunkie/pointinregion.m b/chunkie/pointinregion.m new file mode 100644 index 0000000..61afddb --- /dev/null +++ b/chunkie/pointinregion.m @@ -0,0 +1,19 @@ +function [nin] = pointinregion(cgrph,rgn,r0) + nin = 0; + for ii=1:numel(rgn) + iedges = rgn{ii}; + rs = []; + for jj=1:numel(iedges) + rtmp = sort(cgrph.echnks(abs(iedges(jj)))).r(:,:); + if (iedges(jj)<0) + rtmp = fliplr(rtmp(:,:)); + end + rs = [rs,rtmp]; + end + [in] = inpolygon(r0(1),r0(2),rs(1,:),rs(2,:)); + if (in == 1) + nin = nin + 1; + end + end +end + diff --git a/chunkie/regioninside.m b/chunkie/regioninside.m new file mode 100644 index 0000000..db32ab0 --- /dev/null +++ b/chunkie/regioninside.m @@ -0,0 +1,20 @@ +function [isinside] = regioninside(cgrph,rgn1,rgn2) + + e2 = rgn2{1}{1}(1); + v2 = find(cgrph.verts2edge(:,abs(e2))==1); + v2 = cgrph.verts(:,v2); + irgn = 0; + for ii=2:numel(rgn1) + nin = pointinregion(cgrph,rgn1{ii},v2); + disp("first inclusion:") + nin + if (nin > 0 && mod(nin,2)==1) + if (irgn ~= 0) + disp("Warning: an unsupported geometry error has occurred"); + end + irgn = ii; + end + end + isinside = (irgn ~=0); +end + diff --git a/devtools/test/chunkgrphregionTest.m b/devtools/test/chunkgrphregionTest.m new file mode 100644 index 0000000..405d872 --- /dev/null +++ b/devtools/test/chunkgrphregionTest.m @@ -0,0 +1,232 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% . . . builds a simple pentagonal chunkergraph +% and tests the interior Helmholtz Dirichlet problem +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%clear all + +addpaths_loc(); + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% . . . builds a simple pentagonal chunkergraph +% and tests the interior Helmholtz Dirichlet problem +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%clear all + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +a = -1.0; +b = 1.0; + +ncurve = 1; + +% set angles for top and bottom curve +theta = [pi/2.2 pi/2.4]; + +% set parametrization start and end points for chunkie objects +tab = [-theta(1)/2 -theta(2)/2; theta(1)/2 theta(2)/2]; + +% set parameters for curve parametrization +verta = [-0.5,-0.5,0.5,0.5;-0.5,0.5,0.5,-0.5]; +vertb = verta*2; +vertc = verta*3; +vertd = vertc; +vertc(1,:) = vertc(1,:)+12; + +evert = [1.1;0]; +verts = [vertd,verta,vertb,vertc,evert]; +v2e = [1,-1,0,0;0,1,-1,0;0,0,1,-1;-1,0,0,1]; +verts2edge = zeros(18,size(verts,2)); +verts2edge(1:16,1:16) = kron(eye(4),v2e); +verts2edge(17,11) = 1; +verts2edge(17,17)=-1; +verts2edge(18,12) = 1; +verts2edge(18,17)= -1; + +fchnks = []; + + +prefs = []; +% prefs.chsmall = 1d-4; +[cgrph] = chunkgraph(verts,verts2edge,fchnks,prefs); + +vstruc = procverts(cgrph); +%rgns = findregions(cgrph); +cgrph = balance(cgrph); + +% rgns = cgrph.regions; +% rgn1 = rgns{1}; +% rgn2 = rgns{2}; +% +% r2ub = rgn2{1}; +% +% e2 = rgn2{1}{1}(1); +% v2 = find(cgrph.verts2edge(:,abs(e2))==1); +% v2 = verts(:,v2); +% +% irgn = 0; +% for ii=1:numel(rgn1) +% nin = pointinregion(cgrph,rgn1{ii},v2); +% if (nin > 0 && mod(nin,2)==1) +% if (irgn ~= 0) +% display("Warning: an unsupported geometry error has occurred"); +% end +% irgn = ii; +% end +% end +% +% if (irgn == 0) +% +% end +% +% rgnout = rgns{1}; +% if (numel(rgns)>1) +% rgn2 = rgns{2}; +% [rgnout] = mergeregions(cgrph,rgnout,rgn2); +% for ii=3:numel(rgns) +% rgn2 = rgns{ii}; +% [rgnout] = mergeregions(cgrph,rgnout,rgn2); +% end +% end +%%%% [in] = inpolygon(xquery,yquery,xverts,yverts) + + + +function [r,d,d2] = circulararc(t,cpars) +%%circulararc +% return position, first and second derivatives of a circular arc +% that passes through points (x,y)=(a,0) and (x,y)=(b,0) with opening +% angle theta0. +% +% Inputs: +% t - paramter values (-theta0/2,theta0/2) to evaluate these quantities +% +% Outputs: +% r - coordinates +% d - first derivatives w.r.t. t +% d2 - second derivatives w.r.t. t + +v0 = cpars.v0; +v1 = cpars.v1; +theta0 = cpars.theta; +ifconvex = cpars.ifconvex; + +a = v0(1); +b = v1(1); + +islocal = -1; +if isfield(cpars,'islocal') + islocal = cpars.islocal; +end + +if islocal == -1 + cx = (a+b)/2; + r0 = (b-a)/2/sin(theta0/2); + + if ifconvex + cy = v0(2)+(b-a)/2/tan(theta0/2); + theta = 3*pi/2+t; + else + cy = v0(2)-(b-a)/2/tan(theta0/2); + theta = pi/2+t; + end + + + xs = r0*cos(theta); + ys = r0*sin(theta); + + xp = -ys; + yp = xs; + + xpp = -xs; + ypp = -ys; + + xs = cx + xs; + ys = cy + ys; + +else + + r0 = (b-a)/2/sin(theta0/2); + if ~ifconvex + if islocal == 0 + cx = r0*cos(pi/2+theta0/2); + sx = r0*sin(pi/2+theta0/2); + elseif islocal == 1 + cx = r0*cos(pi/2-theta0/2); + sx = r0*sin(pi/2-theta0/2); + end + elseif ifconvex + if islocal == 0 + cx = r0*cos(3*pi/2+theta0/2); + sx = r0*sin(3*pi/2+theta0/2); + elseif islocal == 1 + cx = r0*cos(3*pi/2-theta0/2); + sx = r0*sin(3*pi/2-theta0/2); + end + end + +% t2 = t.*t; +% t3 = t2.*t; +% t4 = t3.*t; +% t5 = t4.*t; +% t6 = t5.*t; +% t7 = t6.*t; +% t8 = t7.*t; +% t9 = t8.*t; +% t10 = t9.*t; +% +% +% ct = -t2/2 + t4/24 - t6/720 + t8/40320 - t10/3628800; +% st = t - t3/6 + t5/120 - t7/5040 + t9/362880; + +% better to use sin(t) directly instead of its series expansion because +% 1. the evaluation of sin(t) is accurate at t=0; +% 2. one needs to determine how many terms are needed in series expansion, +% which looks simple but it could be either inefficient or inaccurate +% depending on the value of t; 3. if we write "if" statements, it's +% difficult to vectorize the evaluation. + +% same reason that we should use -2*sin(t/2).^2 instead of its Taylor +% expansion, but of course one should NOT use cos(t)-1. + ct = -2*sin(t/2).^2; + st = sin(t); + + ctp = -st; + stp = cos(t); + + ctpp = -stp; + stpp = -st; + + xs = -sx*st + cx*ct; + ys = cx*st + sx*ct; + + xp = -sx*stp + cx*ctp; + yp = cx*stp + sx*ctp; + + xpp = -sx*stpp + cx*ctpp; + ypp = cx*stpp + sx*ctpp; +end + + +r = [(xs(:)).'; (ys(:)).']; +d = [(xp(:)).'; (yp(:)).']; +d2 = [(xpp(:)).'; (ypp(:)).']; + +end + +function [r,d,d2] = sinearc(t,amp,frq) +xs = t; +ys = amp*sin(frq*t); +xp = ones(size(t)); +yp = amp*frq*cos(frq*t); +xpp = zeros(size(t)); +ypp = -frq*frq*amp*sin(t); + +r = [(xs(:)).'; (ys(:)).']; +d = [(xp(:)).'; (yp(:)).']; +d2 = [(xpp(:)).'; (ypp(:)).']; +end From 5a551de92f836bbbb33fe59be2e197c2f94753f6 Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Wed, 26 Jul 2023 21:17:08 -0400 Subject: [PATCH 07/23] fix documentation of chunkerfunc, small update to guide --- chunkie/chunkerfunc.m | 7 +++---- docs/guide/chunkers.rst | 36 +++++++++++++++++++++++++++++++++--- 2 files changed, 36 insertions(+), 7 deletions(-) diff --git a/chunkie/chunkerfunc.m b/chunkie/chunkerfunc.m index 88790d9..c069f8c 100644 --- a/chunkie/chunkerfunc.m +++ b/chunkie/chunkerfunc.m @@ -13,7 +13,7 @@ % [r,d] = fcurve(t); or [r,d,d2] = fcurve(t); % where d is the first derivative of r with respect to t and % d2 is the second derivative. in some situations, this will -% improve the convergence order. +% improve the convergence order and final precision. % % Optional input: % cparams - curve parameters structure (defaults) @@ -25,9 +25,8 @@ % ifclosed == 0 (Inf) % cparams.nover = oversample resolved curve nover % times (0) -% cparams.eps = resolve coordinates, arclength, -% and first and second derivs of coordinates -% to this tolerance (1.0e-6) +% cparams.eps = tolerance to resolve coordinates and arclength +% density (1.0e-6) % cparams.lvlr = string, determines type of level % restriction to be enforced % lvlr = 'a' -> no chunk should have double the arc length diff --git a/docs/guide/chunkers.rst b/docs/guide/chunkers.rst index 763d69b..6cab91f 100644 --- a/docs/guide/chunkers.rst +++ b/docs/guide/chunkers.rst @@ -2,7 +2,37 @@ Curve Discretization with Chunkers =================================== -In chunkie, a smooth, regular curve is discretized as a -chunker object. The curve is divided up into "chunks" of -curve, each discretized by scaled Legendre nodes. +In chunkie, a smooth, regular curve is discretized by diving +it into pieces, called "chunks", which are then represented +by a polynomial interpolant at scaled Legendre nodes. This +information is stored in a chunker object. + +A chunker object can be obtained from a curve parameterization +using the function chunkerfunc. The chunker class overloads +some MATLAB commands, like plot and quiver, to simplify common +visualization tasks. The code below creates a chunker object +for a circle and plots the geometry and the normal vectors. + +.. code:: matlab + + % chunk up circle + + r = 0.7; ctr = [1.0;-0.5]; + circfun = @(t) ctr + r*[cos(t(:).');sin(t(:).')]; + + chnkr = chunkerfunc(circfun); + + % plot curve, nodes, and normals + + figure() + plot(chnkr,'r-x') + hold on + quiver(chnkr,'b') + +.. image:: ../assets/images/guide/chunkers_circle.png + :width: 350px + :alt: circle chunker + :align: center + + From 3ed301d68621b9d23458642f2233f9dc7578793f Mon Sep 17 00:00:00 2001 From: jghoskins Date: Thu, 27 Jul 2023 10:31:18 -0500 Subject: [PATCH 08/23] bug fixes in poset nonsense --- chunkie/@chunkgraph/chunkgraph.m | 14 ++++++++++++++ devtools/test/chunkgrphregionTest.m | 2 +- 2 files changed, 15 insertions(+), 1 deletion(-) diff --git a/chunkie/@chunkgraph/chunkgraph.m b/chunkie/@chunkgraph/chunkgraph.m index 76c6c8a..fd48d34 100644 --- a/chunkie/@chunkgraph/chunkgraph.m +++ b/chunkie/@chunkgraph/chunkgraph.m @@ -161,6 +161,20 @@ end + rgns = regions; + rgnso= {}; + + for ii=1:max(s) + inds = find(s==ii); + rgnout = rgns{inds(1)}; + for jj=2:numel(inds) + indj = inds(jj); + [rgnout] = mergeregions(obj,rgnout,rgns{indj}); + end + rgnso{ii} = rgnout; + end + + regions = rgnso; rgns = regions; rgnout = rgns{1}; if (numel(rgns)>1) diff --git a/devtools/test/chunkgrphregionTest.m b/devtools/test/chunkgrphregionTest.m index 405d872..0ede369 100644 --- a/devtools/test/chunkgrphregionTest.m +++ b/devtools/test/chunkgrphregionTest.m @@ -38,7 +38,7 @@ vertc(1,:) = vertc(1,:)+12; evert = [1.1;0]; -verts = [vertd,verta,vertb,vertc,evert]; +verts = [vertc,vertd,vertb,verta,evert]; v2e = [1,-1,0,0;0,1,-1,0;0,0,1,-1;-1,0,0,1]; verts2edge = zeros(18,size(verts,2)); verts2edge(1:16,1:16) = kron(eye(4),v2e); From b745c16972720e758e7e001771f934ff1f1b4fca Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Fri, 28 Jul 2023 17:19:30 -0400 Subject: [PATCH 09/23] build out chunker section of guide, update documentation of class and chunkerfunc --- chunkie/@chunker/chunker.m | 79 ++++++++- chunkie/chunkerfunc.m | 3 + chunkie/guide/addpaths_loc.m | 4 + chunkie/guide/guide_chunkers.m | 129 ++++++++++++++ chunkie/guide/guide_chunkers_barbell.png | Bin 0 -> 24172 bytes chunkie/guide/guide_chunkers_bymode.png | Bin 0 -> 56804 bytes chunkie/guide/guide_chunkers_circle.png | Bin 0 -> 39560 bytes chunkie/guide/guide_chunkers_interior.png | Bin 0 -> 11971 bytes .../guide/guide_chunkers_shiftandreverse.png | Bin 0 -> 54139 bytes chunkie/guide/guide_chunkers_starfish.png | Bin 0 -> 61687 bytes chunkie/starfish.m | 36 ++-- docs/guide.rst | 8 + docs/guide/chunkers.rst | 157 +++++++++++++++--- docs/index.rst | 2 + 14 files changed, 384 insertions(+), 34 deletions(-) create mode 100644 chunkie/guide/addpaths_loc.m create mode 100644 chunkie/guide/guide_chunkers.m create mode 100644 chunkie/guide/guide_chunkers_barbell.png create mode 100644 chunkie/guide/guide_chunkers_bymode.png create mode 100644 chunkie/guide/guide_chunkers_circle.png create mode 100644 chunkie/guide/guide_chunkers_interior.png create mode 100644 chunkie/guide/guide_chunkers_shiftandreverse.png create mode 100644 chunkie/guide/guide_chunkers_starfish.png diff --git a/chunkie/@chunker/chunker.m b/chunkie/@chunker/chunker.m index 80340fa..ae5a8be 100644 --- a/chunkie/@chunker/chunker.m +++ b/chunkie/@chunker/chunker.m @@ -1,8 +1,73 @@ classdef chunker -%CHUNKER class which describes a curve divided into chunks (panels). +%CHUNKER class which describes a curve divided into chunks (or "panels"). +% % On each chunk the curve is represented by the values of its position, -% first and second derivatives in parameter space on a Legendre grid. +% first and second derivatives by scaled Legendre nodes. +% +% chunker properties: +% k - integer, number of Legendre nodes on each chunk +% nch - integer, number of chunks that make up the curve +% dim - integer, dimension of the ambient space in which the curve is +% embedded +% npt - returns k*nch, the total number of points on the curve +% r - dim x k x nch array, r(:,i,j) gives the coordinates of the ith +% node on the jth chunk of the chunker +% h - nch array of scaling factors for chunks. the chunk derivatives are +% scaled as if the coordinates in r(:,:,j) are sampled on an +% interval of length 2*h(j). This affects integration formulas. +% d - dim x k x nch array, d(:,i,j) gives the time derivative of the +% coordinate at the ith node on the jth chunk of the chunker +% d2 - dim x k x nch array, d(:,i,j) gives the 2nd time derivative of the +% coordinate at the ith node on the jth chunk of the chunker +% n - dim x k x nch array of normals to the curve +% data - datadim x k x nch array of data attached to chunker points +% this data will be refined along with the chunker +% adj - 2 x nch integer array. adj(1,j) is i.d. of the chunk that +% precedes chunk j in parameter space. adj(2,j) is the i.d. of the +% chunk which follows. if adj(i,j) is 0 then that end of the chunk +% is a free end. if adj(i,j) is negative than that end of the chunk +% meets with other chunk ends in a vertex. the specific negative +% number acts as an i.d. of that vertex. % +% chunker methods: +% chunker(p,t,w) - construct an empty chunker with given preferences and +% precomputed Legendre nodes/weights (optional) +% obj = addchunk(obj,nchadd) - add nchadd chunks to the structure +% (initialized with zeros) +% obj = makedatarows(obj,nrows) - add nrows rows to the data storage. +% [obj,info] = sort(obj) - sort the chunks so that adjacent chunks are +% stored sequentially +% [rn,dn,d2n,dist,tn,ichn] = nearest(obj,ref,ich,opts,u,xover,aover) - +% find nearest point on chunker to ref +% obj = reverse(obj) - reverse chunk orientation +% rmin = min(obj) - minimum of coordinate values +% rmax = max(obj) - maximum of coordinate values +% wts = weights(obj) - scaled integration weights on curve +% obj.n = normals(obj) - recompute normal vectors +% onesmat = onesmat(obj) - matrix that corresponds to integration of a +% density on the curve +% rnormonesmat = normonesmat(obj) - matrix that corresponds to +% integration of dot product of normal with vector density on +% the curve +% plot(obj,varargin) - plot the chunker curve +% plot3(obj,idata,varargin) - 3D plot of the curve and one row of the +% data storage +% quiver(obj,varargin) - quiver plot of the chnkr points and normals +% scatter(obj,varargin) - scatter plot of the chnkr nodes +% tau = taus(obj) - unit tangents to curve +% obj = refine(obj,varargin) - refine the curve +% a = area(obj) - for a closed curve, area inside +% s = arclength(obj) - get values of arclength along curve +% kappa = signed_curvature(obj) - get signed curvature along curve +% rflag = datares(obj,opts) - check if data in data rows is resolved +% [rc,dc,d2c] = exps(obj) - get expansion coefficients for r,d,d2 +% ier = checkadjinfo(obj) - checks that the adjacency info of the curve +% is consistent +% [inds,adjs,info] = sortinfo(obj) - attempts to sort the curve and finds +% number of connected components, etc +% [re,taue] = chunkends(obj,ich) - get the endpoints of chunks +% flag = flagnear(obj,pts,opts) - flag points near the boundary + % author: Travis Askham (askhamwhat@gmail.com) @@ -47,6 +112,16 @@ methods function obj = chunker(p,t,w) + %CHUNKER construct an empty chunker with some default settings + % + % syntax: chnkr = chunker(p,t,w); + % + % optional input: + % p - struct of preferences + % p.k - integer, order to be used on chunks (16) + % p.dim - integer, dimension of ambient space (2) + % t, w - arrays of Legendre nodes and weights of order p.k + % if nargin < 1 || isempty(p) p = chunkerpref(); else diff --git a/chunkie/chunkerfunc.m b/chunkie/chunkerfunc.m index c069f8c..5ecfcb3 100644 --- a/chunkie/chunkerfunc.m +++ b/chunkie/chunkerfunc.m @@ -41,6 +41,9 @@ % pref.nchmax - maximum number of chunks (10000) % pref.k - number of Legendre nodes on chunks (16) % +% Output: +% chnkr - a chunker object containing the discretization of the domain +% % Examples: % chnkr = chunkerfunc(@(t) starfish(t)); % chunk up starfish w/ standard % % options diff --git a/chunkie/guide/addpaths_loc.m b/chunkie/guide/addpaths_loc.m new file mode 100644 index 0000000..64bc844 --- /dev/null +++ b/chunkie/guide/addpaths_loc.m @@ -0,0 +1,4 @@ +function addpaths_loc() + +addpath('../'); +addpath(genpath('../FLAM')); \ No newline at end of file diff --git a/chunkie/guide/guide_chunkers.m b/chunkie/guide/guide_chunkers.m new file mode 100644 index 0000000..f9edb96 --- /dev/null +++ b/chunkie/guide/guide_chunkers.m @@ -0,0 +1,129 @@ +%GUIDE_CHUNKERS +% +% This script complements the chunkie guide section on chunker objects. +% It shows the most common methods for building and working with chunkers. +% + +addpaths_loc(); +rng(1234); + +%%%%%%%%%%%%% circle +% START CIRCLE +% chunk up circle + +rad = 2; ctr = [1.0;-0.5]; +circfun = @(t) ctr + rad*[cos(t(:).');sin(t(:).')]; + +chnkr1 = chunkerfunc(circfun); + +% plot curve, nodes, and normals + +figure(1) +clf +plot(chnkr1,'b-x') +hold on +quiver(chnkr1,'r') +axis equal tight +% END CIRCLE + +saveas(figure(1),"guide_chunkers_circle.png"); + +%%%%%%%%%%%%% more examples +% START MORE PARAMS +% curvebymode lets you specify a star shaped domain by +% a cosine/sine series for the radius + +modes = randn(11,1); modes(1) = 1.1*sum(abs(modes(2:end))); +ctr = [1.0;-0.5]; +chnkr2 = chunkerfunc(@(t) chnk.curves.bymode(t,modes,ctr)); + +figure(2) +clf +plot(chnkr2,'b-x') +hold on +quiver(chnkr2,'r') +axis equal tight + +% classic starfish domain + +narms = 5; +amp = 0.5; +chnkr3 = chunkerfunc(@(t) starfish(t,narms,amp)); + +figure(3) +clf +plot(chnkr3,'b-x') +hold on +quiver(chnkr3,'r') +axis equal tight +% END MORE PARAMS + +saveas(figure(2),"guide_chunkers_bymode.png"); +saveas(figure(3),"guide_chunkers_starfish.png"); + +%%%%%%%%%%%%% rounded polygons +% START ROUNDED POLY +% roundedpolygon provides a chunk discretization of a rounded polygon + +verts = chnk.demo.barbell(2.0,2.0,1.0,1.0); % vertices of a barbell +chnkr4 = roundedpolygon(verts); + +figure(4) +clf +plot(chnkr4,'b-x') +hold on +quiver(chnkr4,'r') +axis equal tight +% END ROUNDED POLY + +saveas(figure(4),"guide_chunkers_barbell.png"); + +%%%%%%%%%%%%%% working with chunkers + +% START SHIFT AND REVERSE +% make a copy of the random mode domain +chnkr5 = chnkr2; + +% rotate it +theta = pi/4; c = cos(theta); s = sin(theta); U = [c -s; s c]; +chnkr5.r(:,:) = U*chnkr5.r(:,:); % rotating affects position and derivatives +chnkr5.d(:,:) = U*chnkr5.d(:,:); +chnkr5.d2(:,:) = U*chnkr5.d2(:,:); + +% make a copy of the circle domain and shift it +chnkr6 = chnkr1; +chnkr6.r = chnkr6.r + [-0.3;0.4]; % shifting only affects position +% reverse the orientation +chnkr6 = chnkr6.reverse(); + +% merge these two curves into one domain +chnkr7 = merge([chnkr5,chnkr6]); + +figure(5); clf +plot(chnkr7,'b-x'); hold on; quiver(chnkr7,'r') +axis equal tight +% END SHIFT AND REVERSE + +saveas(figure(5),"guide_chunkers_shiftandreverse.png"); + +% START INTERIOR + +% create a grid of points +mins = min(chnkr7); maxs = max(chnkr7); +x1 = linspace(mins(1),maxs(1)); y1 = linspace(mins(2),maxs(2)); +[xx,yy] = meshgrid(x1,y1); +pts = [xx(:).'; yy(:).']; + +% find the points inside the merged domain +in = 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zPbGJhL(|9EW7R$I{0;a8DaVE5_wSyQdS1s01I=$aFd@arjlUD*3 Date: Fri, 28 Jul 2023 17:20:00 -0400 Subject: [PATCH 10/23] add better name for future of rounded polygons in chunkie --- chunkie/roundedpolygon.m | 262 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 262 insertions(+) create mode 100644 chunkie/roundedpolygon.m diff --git a/chunkie/roundedpolygon.m b/chunkie/roundedpolygon.m new file mode 100644 index 0000000..867e3ca --- /dev/null +++ b/chunkie/roundedpolygon.m @@ -0,0 +1,262 @@ +function chnkr = roundedpolygon(verts,cparams,pref,edgevals) +%CHUNKPOLY return a chunker object corresponding to the polygon with the +% given vertices. By default, a polygon with rounded corners is returned. +% Open and higher dimensional "polygons" are allowed. Optional dyadic +% refinement near corners of true polygons (no rounding). +% +% Syntax: chnkr = chunkpoly(verts,cparams,pref,edgevals) +% +% Input: +% verts - (dimv,nverts) array of "polygon" vertices +% in order +% +% Optional input: +% cparams - options structure +% cparams.rounded = true if corner rounding is to be used. +% false if no rounding is used (true) +% cparams.widths = radius around each corner point where either the +% rounding or dyadic refinement is applied +% (defaults to 1/10th of minimum +% of length of adjoining edges) +% cparams.autowidths = automatically compute widths (false) +% cparams.autowidthsfac = if using autowidths, set widths +% to autowidthsfac*minimum of adjoining +% edges (0.1) +% cparams.ifclosed = true, if it's a closed polygon +% false, if it's an open segment (true) +% cparams may also specify any of the values to send to the +% refine routine, otherwise it is called with defaults +% +% ~ Rounding parameters ~ +% cparams.eps - resolve curve to tolerance eps +% resolve coordinates, arclength, +% and first and second derivs of coordinates +% to this tolerance (1.0e-6) +% +% pref - chunkerpref object/ preference structure +% pref.k determines order of underlying Legendre nodes +% edgevals - very optional input. specifies constant values along each +% edge. The routine then stores a smoothed interpolant +% of these edge values on the rounded structure in the +% output chunker's data field +% +% Output: +% chnkr - chunker object corresponding to (rounded) polygon +% +% Examples: +% barbell_verts = chnk.demo.barbell(); +% chnkr = roundedpolygon(barbell_verts); % rounded "barbell" domain +% % with standard options +% cparams = []; cparams.rounded = false; +% pref = []; pref.k = 30; +% chnkr = chunkpoly(barbell_verts,cparams,pref); % not rounded +% +% See also CHUNKERFUNC, CHUNKER, CHUNKERPREF, REFINE + +[dimv,nv] = size(verts); + +assert(dimv > 1) + +if nargin < 2 + cparams = []; +end +if nargin < 3 + p = []; + p.dim = dimv; + pref = chunkerpref(p); +else + pref = chunkerpref(pref); + if pref.dim ~= dimv + warning('dimensions dont match, overwriting with vertex dim'); + pref.dim = dimv; + end +end +if nargin < 4 + edgevals = []; +end + +autowidths = false; +autowidthsfac = 0.1; +ifclosed = true; +eps = 1e-6; +nover = 0; + +if isfield(cparams,'ifclosed') + ifclosed = cparams.ifclosed; +end +if isfield(cparams,'eps') + eps = cparams.eps; +end +if isfield(cparams,'nover') + nover = cparams.nover; +end + +if (ifclosed) + verts2 = [verts(:,end), verts, verts(:,1)]; + edges2 = sqrt(sum(diff(verts2,1,2).^2,1)); +else + edges2 = [0, sqrt(sum(diff(verts,1,2).^2,1)), 0]; +end + +widths_not_set = true; + +if isfield(cparams,'widths') + widths = cparams.widths; + widths_not_set = false; +end +if isfield(cparams,'autowidths') + autowidths = cparams.autowidths; +end +if isfield(cparams,'autowidthsfac') + autowidthsfac = cparams.autowidthsfac; +end + +if (autowidths || widths_not_set) + widths = autowidthsfac*... + min(edges2(1:end-1),edges2(2:end)); +end + +if ifclosed + widths = [widths(:); widths(1)]; + verts = [verts, verts(:,1)]; + nv = size(verts,2); +end + +nedge = nv - 1; +nvals = 0; +if numel(edgevals) ~= 0 + assert(rem(numel(edgevals),nedge) == 0, ... + 'number of edge values should be multiple of number of edges'); + nvals = numel(edgevals)/nedge; + edgevals = reshape(edgevals,nvals,nedge); +end + +chnkr = chunker(pref); +chnkr = chnkr.makedatarows(nvals); +k = chnkr.k; dim = chnkr.dim; +[t,w] = lege.exps(k); +onek = ones(k,1); + + +if nvals > 0 + aint = lege.intmat(chnkr.k); +end + +for i = 1:nv-1 + % grab vertices + r1 = verts(:,i); r2 = verts(:,i+1); + w1 = widths(i); w2 = widths(i+1); + l = sqrt(sum((r1-r2).^2)); + assert(l > w1+w2+2*eps(1)*l,'widths too large for side'); + + % make chunk in middle + v = (r2-r1)/l; + ts = w1+(l-w2-w1)*(t+1)/2.0; + chnkr = chnkr.addchunk(); + nch = chnkr.nch; + if nvals > 0 + val1 = edgevals(:,i); + chnkr.data(:,:,nch) = bsxfun(@times,val1,onek(:).'); + end + chnkr.r(:,:,nch) = r1 + bsxfun(@times,v(:),(ts(:)).'); + chnkr.d(:,:,nch) = repmat(v(:),1,k); + chnkr.d2(:,:,nch) = zeros(dim,k); + chnkr.adj(1,nch) = 0; chnkr.adj(2,nch) = 0; + if nch > 1 + chnkr.adj(1,nch) = nch-1; + chnkr.adj(2,nch-1) = nch; + end + chnkr.h(nch) = (l-w2-w1)/2.0; + + if or(i < nv-1,ifclosed) + % chunk up smoothed corner made by three verts + if (i==nv-1) + if nvals > 0 + val2 = edgevals(:,1); + end + r3 = verts(:,2); + else + if nvals > 0 + val2 = edgevals(:,i+1); + end + r3 = verts(:,i+2); + end + l2 = sqrt(sum((r2-r3).^2)); + v = -v; + v2 = (r3-r2)/l2; + cosphi = dot(v2,v); %cosine of angle between edges + sinphi = sqrt(1-cosphi*cosphi); + trange = w2*sqrt((1-cosphi)/2); %parameter space range of gaussian + hbell = abs(trange)/8.0; % width parameter of gaussian + m = sinphi/(1-cosphi); % slope of abs approx + cpt.ta = -trange; + cpt.tb = trange; + cpt.eps = eps; cpt.levrestr = 0; cpt.ifclosed = 0; + chnkrt = sort(chunkerfunc(@(t)fround(t,m,hbell,dim),cpt,pref)); + + % do optimal procrustes match of left and right ends + rl = fround(-trange,m,hbell,dim); rr = fround(trange,m,hbell,dim); + [um,~,vm] = svd([w2*v w2*v2]*([rl rr].')); + rotmat = um*vm.'; + + % copy in rotated and translated chunks + ncht = chnkrt.nch; + chnkr = chnkr.addchunk(ncht); + chnkr.r(:,:,nch+1:nch+ncht) = reshape(rotmat*chnkrt.r(:,:),dim,k,ncht)+r2; + chnkr.d(:,:,nch+1:nch+ncht) = reshape(rotmat*chnkrt.d(:,:),dim,k,ncht); + chnkr.d2(:,:,nch+1:nch+ncht) = reshape(rotmat*chnkrt.d2(:,:),dim,k,ncht); + chnkr.adj(:,nch+1:nch+ncht) = chnkrt.adj+nch; + chnkr.adj(2,nch) = nch+1; + chnkr.adj(1,nch+1) = nch; + chnkr.h(nch+1:nch+ncht) = chnkrt.h; + + if nvals > 0 + ds = bsxfun(@times,reshape(sum((rotmat*chnkrt.d(:,:)).^2,1),k,ncht), ... + (chnkrt.h(:)).'); + dsw = bsxfun(@times,w(:),ds); + dssums = sum(dsw,1); + dssums2 = cumsum([0,dssums(1:end-1)]); + dsint = aint*ds; + dsint = bsxfun(@plus,dsint,dssums2); + lencorner = sum(dsw(:)); + ss = -lencorner/2.0 + dsint; + ss = ss/lencorner*16; + erfss = erf(ss); + datass = reshape((val2(:)-val1(:))/2*((erfss(:)).'+1) ... + +val1(:),nvals,k,ncht); + chnkr.data(:,:,nch+1:nch+ncht) = datass; + end + end + +end + +if ifclosed + nch = chnkr.nch; + chnkr.adj(1,1) = nch; + chnkr.adj(2,nch) = 1; +end + +chnkr = chnkr.refine(cparams); + +% compute normals + +chnkr.n = normals(chnkr); + +end + +function [r,d,d2] = fround(t,m,h,dim) + +[y,dy,d2y] = chnk.spcl.absconvgauss(t,m,0.0,h); + +r = zeros(dim,length(t)); +d = zeros(dim,length(t)); +d2 = zeros(dim,length(t)); + +r(1,:) = t; +r(2,:) = y; +d(1,:) = 1.0; +d(2,:) = dy; +d2(1,:) = 0.0; +d2(2,:) = d2y; + +end From e18bd2abb62392aaccc41ebb1fb98016e34c0e0d Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Fri, 28 Jul 2023 17:21:22 -0400 Subject: [PATCH 11/23] fix typo --- docs/guide/chunkers.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/guide/chunkers.rst b/docs/guide/chunkers.rst index 15f2fab..d306bf5 100644 --- a/docs/guide/chunkers.rst +++ b/docs/guide/chunkers.rst @@ -5,9 +5,9 @@ Curve Discretization with Chunkers =================================== -In chunkie, a smooth, regular curve is discretized by diving +In chunkie, a smooth, regular curve is discretized by dividing it into pieces, called "chunks", which are then represented -by a polynomial interpolant at scaled Legendre nodes. This +by polynomial interpolants at scaled Legendre nodes. This information is stored in a :matlab:`chunker` object. Creating a Chunker From eee4baf7923772ccceb371b49b863baf3a76c196 Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Mon, 31 Jul 2023 12:35:46 -0400 Subject: [PATCH 12/23] progress on the simplebvps section --- docs/guide/simplebvps.rst | 101 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 101 insertions(+) diff --git a/docs/guide/simplebvps.rst b/docs/guide/simplebvps.rst index b912ed4..ee20d02 100644 --- a/docs/guide/simplebvps.rst +++ b/docs/guide/simplebvps.rst @@ -1,7 +1,83 @@ +.. role:: matlab(code) + :language: matlab + Solving Standard Boundary Value Problems ========================================= +Chunkie uses the integral equation method to solve PDEs. +In contrast with finite element methods, where the PDE is +typically converted to a weak form, the standard approach for +an integral equation method is to select an integral representation +of the solution that satisfies the PDE inside the domain +*a priori*. This cannot be done for just any PDE; typically, +integral equation methods are limited to constant coefficient, +homogeneous PDEs. But when the methods apply, they are +efficient and accurate. + +The following is a very high level discussion of the main ideas. +Some more specific examples are included further below. +For more, see, *inter alia*, [Rok1985]_, [CK2013]_, [GL1996]_, and +[Poz1992]_. + +Let :math:`\Omega` be a domain with boundary :math:`\Gamma`. +Suppose that we are interested in the solution of the boundary +value problem + +.. math:: + + \begin{align*} + \mathcal{L} u &= 0 & \textrm{ in } \Omega \; ,\\ + \mathcal{B} u &= f & \textrm{ on } \Gamma \; , + \end{align*} + +where :math:`\mathcal{L}` is a linear, constant coefficient PDE +operator and :math:`\mathcal{B}` is a linear trace operator that +restricts :math:`u`, or some linear operator applied to :math:`u`, to the +boundary. + +Suppose that :math:`G` is the Green function for :math:`\mathcal{L}` +and let :math:`K` be an integral kernel that is a linear +operator applied to :math:`G`. Then, :math:`u` can be represented +as a *layer potential*, i.e. it can be written in the form + +.. math:: + + u(x) = \int_\Gamma K(x,y) \sigma(y) \, ds(y) \; , + +which has the property that :math:`u` automatically solves the PDE +for any choice of density :math:`\sigma` (defined on the boundary +alone). The idea is to then solve for a specific :math:`\sigma` +for which the boundary condition holds: + +.. math:: + + \mathcal{B} \left [ \int_\Gamma K(\cdot,y)\sigma(y)\, ds(y) \right ] + = f \textrm{ on } \Gamma \; . + +Some of the art in the design of an integral equation method is +in choosing :math:`K` so that the above yields a reasonable boundary +integral equation for :math:`\sigma`. Fortunately, there is a +large literature on good quality integral representations for the most +common problems in classical physics (linear elasticity, electrostatics, +acoustics, and fluid flow). We include some examples below. + +This integral equation can then be discretized. Chunkie employs a +Nyström discretization method, i.e. the unknown :math:`\sigma` +is represented by its values at the nodes of a :matlab:`chunker` +object. Because :math:`K` is defined in terms of the Green function +for :math:`\mathcal{L}` it often has mild (or even strong) singularities +when restricted to :math:`\Gamma`. One of the key features of +chunkie is that the function :matlab:`layermat` will automatically return +a Nyström discretization of a layer potential using high-order +accurate quadrature rules [BGR2010]_. + +After solving the discrete system for :math:`\sigma`, the PDE solution, +:math:`u`, can then be recovered by evaluating the layer potential +representation at any points of interest. This integral is nearly singular +for points near the boundary. Chunkie provides the function +:matlab:`layereval` for doing this accurately, employing adaptive +integration when necessary. A Laplace Problem @@ -9,6 +85,7 @@ A Laplace Problem + A Helmholtz Scattering Problem ------------------------------- @@ -18,4 +95,28 @@ A Stokes Flow Problem ---------------------- +References +------------ + +.. [Rok1985] Rokhlin, Vladimir. "Rapid solution of integral equations + of classical potential theory." Journal of Computational + Physics 60.2 (1985): 187-207. + + +.. [Poz1992] Pozrikidis, Constantine. *Boundary integral and singularity + methods for linearized viscous flow*. Cambridge University + Press, 1992. + + +.. [GL1996] Guenther, Ronald B., and John W. Lee. *Partial differential + equations of mathematical physics and integral equations*. + Courier Corporation, 1996. + +.. [CK2013] Colton, David, and Rainer Kress. *Integral equation + methods in scattering theory*. Society for Industrial + and Applied Mathematics, 2013. +.. [BGR2010] Bremer, James, Zydrunas Gimbutas, and Vladimir Rokhlin. + "A nonlinear optimization procedure for generalized Gaussian + quadratures." SIAM Journal on Scientific Computing 32.4 (2010): + 1761-1788. From 636243293691fe5c6ce934f8d282dbc55f06e21d Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Tue, 1 Aug 2023 08:22:24 -0400 Subject: [PATCH 13/23] starting on simplebvps part of guide --- docs/guide/simplebvps.rst | 147 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 147 insertions(+) diff --git a/docs/guide/simplebvps.rst b/docs/guide/simplebvps.rst index ee20d02..c5d70fc 100644 --- a/docs/guide/simplebvps.rst +++ b/docs/guide/simplebvps.rst @@ -83,14 +83,161 @@ integration when necessary. A Laplace Problem ------------------ +Consider the Laplace Neumann boundary value problem: +.. math:: + + \begin{align*} + \Delta u &= 0 & \textrm{ in } \Omega \; ,\\ + \frac{\partial u}{\partial n} &= f & \textrm{ on } \Gamma \; , + \end{align*} + +where :math:`n` is the outward normal. +This is a model for the equilibrium heat distribution in a +homogeneous medium, where :math:`f` is a prescribed heat +flux along the boundary. + +For a solution to exist, :math:`f` must satisfy the compatibility +condition: + +.. math:: + + \int_\Gamma f(y) \, ds(y) = 0 \; , + +which is equivalent to requiring that there is no net flux +of heat into the body. +When solutions exist, they are not unique because adding a +constant to any solution gives another solution. + + +The solution of this problem by layer potentials has been +well understood for some time. The standard method is reviewed +here with a fair amount of detail. Users familiar with the +approach may simply want to skip down to the code example. + +The Green function for the Laplace equation is + +.. math:: + + G_0 (x,y) = -\frac{1}{2\pi} \log |x-y| + +The standard choice for the layer potential for this problem is +the *single layer potential* + +.. math:: + u(x) = [S\sigma](x) := \int_\Gamma G_0(x,y) \sigma(y) ds(y) \; . + +Then, imposing the boundary conditions on this representation +results in the equation + +.. math:: + + \begin{align*} + f(x_0) &= \lim_{x\in \Omega, x\to x_0} n(x_0)\cdot \nabla_x + \int_\Gamma G_0(x,y) \sigma(y) \, ds(y) \\ + &= \frac{1}{2} \sigma(x_0) + P.V. \int_\Gamma n(x_0) \cdot \nabla_x G_0(x_0,y) + \sigma(y) \, ds(y) \\ + &=: \left [\left ( \frac{1}{2} \mathcal{I} + \mathcal{S}' \right ) \sigma + \right ] (x_0) \; , + \end{align*} + +where :math:`P.V.` indicates that the integral should be interpreted +in the principal value sense, :math:`\mathcal{I}` is the identity operator, and +the calligraphic letters indicate that these operators act +on functions defined on :math:`\Gamma`. The second equality above uses +a so-called "jump condition" for the single layer potential. + +It turns out that the equation for :math:`\sigma` above is a second-kind +integral equation, i.e. of the form "identity plus compact", but it +is not invertible. This has a simple remedy. The equation + +.. math:: + + f = \left ( \frac{1}{2} \mathcal{I} + \mathcal{S}' + \mathcal{W} \right) \sigma \; , + +where + +.. math:: + + [\mathcal{W}\sigma](x) = \int_\Gamma \sigma (y) \, ds(y) \; , + +has the same solutions as the original equation (so long as +:math:`f` satisfies the compatibility condition) and is +invertible. The operator :math:`\mathcal{W}` is straightforward +to discretize: + +.. math:: + + W = \begin{bmatrix} 1 \\ 1 \\ \vdots \\ 1 \end{bmatrix} + \begin{bmatrix} w_1 & w_2 & \cdots & w_n \end{bmatrix} \; , + +where :math:`w_1,\ldots,w_n` are scaled integration weights on :math:`\Gamma`. +For historical reasons, the routine that returns this matrix +in chunkie is called :matlab:`onesmat`. + +To discretize the boundary integral equation, chunkie requires a +:matlab:`chunker` class object discretization of the boundary and a +:matlab:`kernel` class object representing the integral kernel. +Many of the most common kernel types are available in chunkie, +including the normal derivative of the single layer kernel, which is +called "sprime". This can be obtained via + +.. include:: ../../chunkie/guide/guide_simplebvps.m + :literal: + :code: matlab + :start-after: % START SPRIME + :end-before: % END SPRIME + +The most essential thing that an instance of the kernel class tells chunkie +is how to evaluate the kernel function. This is stored in the field +:matlab:`obj.eval`. The object can also store other information about +the kernel, such as fast algorithms for its evaluation or the type +of singularity it has. + +.. note:: + + The :matlab:`obj.eval` function in a kernel is expected to be + of the form :matlab:`eval(s,t)`, where :matlab:`s` and :matlab:`t` + are structs that specify information about the "sources" and "targets" + for which the kernel is being evaluated. This has the unfortunate feature + that :math:`x` and :math:`y` take the roles of "target" and "source", + respectively, in the math notation above, so the order is reversed. + + The structs :matlab:`s` and :matlab:`t` must have the fields + :matlab:`s.r` and :matlab:`t.r` which specify the + locations of the sources and targets, respectively. + For sources/targets on a :matlab:`chunker` + object, these will also contain fields :matlab:`s.d`, :matlab:`s.d2`, + :matlab:`s.n`, and :matlab:`s.data` (likewise for :matlab:`t`) containing + the chunk information for the corresponding points. For example, + the kernel :matlab:`kernsp` defined above is only defined for targets + on a :matlab:`chunker` discretization of a curve and the kernel evaluator + :matlab:`kernsp.eval` assumes that the field :matlab:`t.n` is populated + with the normal vectors at the targets. + +Because these standard kernels are built into chunkie, this PDE +can be solved with very little coding: + +.. include:: ../../chunkie/guide/guide_simplebvps.m + :literal: + :code: matlab + :start-after: % START LAPLACE NEUMANN + :end-before: % END LAPLACE NEUMANN + + +.. image:: ../../chunkie/guide/guide_simplebvps_laplaceneumann.png + :width: 500px + :alt: combined chunker + :align: center + A Helmholtz Scattering Problem ------------------------------- + A Stokes Flow Problem ---------------------- From a1e7729b7fc1563acee9418989755ee6174b805d Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Tue, 1 Aug 2023 08:23:13 -0400 Subject: [PATCH 14/23] supporting files for guide --- chunkie/guide/guide_simplebvps.m | 51 ++++++++++++++++++ .../guide/guide_simplebvps_laplaceneumann.png | Bin 0 -> 59609 bytes 2 files changed, 51 insertions(+) create mode 100644 chunkie/guide/guide_simplebvps.m create mode 100644 chunkie/guide/guide_simplebvps_laplaceneumann.png diff --git a/chunkie/guide/guide_simplebvps.m b/chunkie/guide/guide_simplebvps.m new file mode 100644 index 0000000..25209f0 --- /dev/null +++ b/chunkie/guide/guide_simplebvps.m @@ -0,0 +1,51 @@ +%GUIDE_SIMPLEBVPS +% +% This script complements the chunkie guide section on simple boundary +% problems. +% It shows how to discretize some common PDEs using chunkie +% + +addpaths_loc(); +rng(1234); + +% START SPRIME +kernsp = kernel('lap','sprime'); +% END SPRIME + +% START LAPLACE NEUMANN +% get a chunker discretization of a starfish domain +chnkr = chunkerfunc(@(t) starfish(t)); + +% define a boundary condition. because of the symmetries of the +% starfish, this function integrates to zero +f = @(r) r(1,:).^2.*r(2,:); +rhs = f(chnkr.r); rhs = rhs(:); + +% get the kernel +kernsp = kernel('lap','sprime'); + +% get a matrix discretization of the boundary integral equation +sysmat = chunkermat(chnkr,kernsp); % just the sprime part +% add the identity term and "ones matrix" +sysmat = sysmat + 0.5*eye(chnkr.npt) + onesmat(chnkr); + +% solve the system +sigma = gmres(sysmat,rhs); + +% grid for plotting solution +x1 = linspace(-2,2,300); +[xx,yy] = meshgrid(x1,x1); +targs = [xx(:).'; yy(:).']; +in = chunkerinterior(chnkr,targs); +uu = nan(size(xx)); + +% need the single layer, not it's dervative, to evaluate u +kerns = kernel('lap','s'); +uu(in) = chunkerkerneval(chnkr,kerns,sigma,targs(:,in)); + +% plot +figure(1); clf +h = pcolor(xx,yy,uu); set(h,'EdgeColor','none'); colorbar +% END LAPLACE NEUMANN +saveas(figure(1),"guide_simplebvps_laplaceneumann.png") + diff --git a/chunkie/guide/guide_simplebvps_laplaceneumann.png b/chunkie/guide/guide_simplebvps_laplaceneumann.png new file mode 100644 index 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zes+M`u{cDvtf|Y>@i=p?%Dp^Jr{EfW23e?lSB-@u3(~TaDIw!wvd%EzC{7n5wqfdw zRe6}KH&WQ_yokaaL(m{1mGO{Mut2Y@sPI8g%#1%c(&JjwaWOh6e)tqa`$XKpt3E08 l>FC=3zxkhAkn#@-IpPv)H2<`@4HFPCGqy0wHTdP&KL91;mdgMD literal 0 HcmV?d00001 From 7fc4ef43f836ddaa97ffbde6dff9215c024eb034 Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Wed, 30 Aug 2023 15:05:18 -0400 Subject: [PATCH 15/23] update paths --- chunkie/demo/addpaths_loc.m | 3 +- chunkie/demo/demo_scatter.m | 50 +++++++++++++++++--------------- chunkie/guide/guide_simplebvps.m | 3 ++ 3 files changed, 32 insertions(+), 24 deletions(-) diff --git a/chunkie/demo/addpaths_loc.m b/chunkie/demo/addpaths_loc.m index 64bc844..33bbc53 100644 --- a/chunkie/demo/addpaths_loc.m +++ b/chunkie/demo/addpaths_loc.m @@ -1,4 +1,5 @@ function addpaths_loc() addpath('../'); -addpath(genpath('../FLAM')); \ No newline at end of file +addpath(genpath('../FLAM')); +addpath('../fmm2d/matlab/'); \ No newline at end of file diff --git a/chunkie/demo/demo_scatter.m b/chunkie/demo/demo_scatter.m index 240383d..9f1a716 100644 --- a/chunkie/demo/demo_scatter.m +++ b/chunkie/demo/demo_scatter.m @@ -11,7 +11,7 @@ % planewave vec -kvec = 20*[1;-1.5]; +kvec = 10*[1;-1.5]; % @@ -101,42 +101,46 @@ figure(2) clf -subplot(1,3,1) + +t = tiledlayout(1,3,'TileSpacing','compact'); + +nexttile zztarg = nan(size(xxtarg)); zztarg(out) = uin; h=pcolor(xxtarg,yytarg,imag(zztarg)); set(h,'EdgeColor','none') +clim([-maxu,maxu]) +colormap(brewermap([],'RdBu')); hold on -plot(chnkr,'LineWidth',2) -axis equal -axis tight -colormap(redblue) -caxis([-maxu,maxu]) -title('$u_{in}$','Interpreter','latex','FontSize',24) - +plot(chnkr,'k','LineWidth',2) +axis equal tight +set(gca, "box","off","Xtick",[],"Ytick",[]); +title('$u^{\textrm{inc}}$','Interpreter','latex','FontSize',12) -subplot(1,3,2) +nexttile zztarg = nan(size(xxtarg)); zztarg(out) = uscat; h=pcolor(xxtarg,yytarg,imag(zztarg)); set(h,'EdgeColor','none') +clim([-maxu,maxu]) +colormap(brewermap([],'RdBu')); hold on -plot(chnkr,'LineWidth',2) -axis equal -axis tight -colormap(redblue) -caxis([-maxu,maxu]) -title('$u_{scat}$','Interpreter','latex','FontSize',24) +plot(chnkr,'k','LineWidth',2) +axis equal tight +set(gca, "box","off","Xtick",[],"Ytick",[]); + +title('$u^{\textrm{scat}}$','Interpreter','latex','FontSize',12) -subplot(1,3,3) +nexttile zztarg = nan(size(xxtarg)); zztarg(out) = utot; h=pcolor(xxtarg,yytarg,imag(zztarg)); set(h,'EdgeColor','none') +clim([-maxu,maxu]) +colormap(brewermap([],'RdBu')); hold on -plot(chnkr,'LineWidth',2) -axis equal -axis tight -colormap(redblue) -caxis([-maxu,maxu]) -title('$u_{tot}$','Interpreter','latex','FontSize',24) +plot(chnkr,'k','LineWidth',2) +axis equal tight +set(gca, "box","off","Xtick",[],"Ytick",[]); + +title('$u^{\textrm{tot}}$','Interpreter','latex','FontSize',12) diff --git a/chunkie/guide/guide_simplebvps.m b/chunkie/guide/guide_simplebvps.m index 25209f0..5d02360 100644 --- a/chunkie/guide/guide_simplebvps.m +++ b/chunkie/guide/guide_simplebvps.m @@ -49,3 +49,6 @@ % END LAPLACE NEUMANN saveas(figure(1),"guide_simplebvps_laplaceneumann.png") +% START BASIC SCATTERING + +% END BASIC SCATTERING From 323fe969a35a3870a2300de88d5a5dab1d1418ed Mon Sep 17 00:00:00 2001 From: jghoskins <32715900+jghoskins@users.noreply.github.com> Date: Tue, 31 Oct 2023 13:01:09 -0400 Subject: [PATCH 16/23] removed verts2edge --- chunkie/@chunkgraph/chunkgraph.m | 24 +++++++++---------- chunkie/@chunkgraph/findregions.m | 4 ++-- chunkie/@chunkgraph/vertextract.m | 4 ++-- chunkie/chunkgraphinit.m | 18 +++++++------- chunkie/mergeregions.m | 4 ++-- chunkie/regioninside.m | 2 +- devtools/test/chunkgrphconstructTest.m | 16 ++++++------- devtools/test/chunkgrphrcipTest.m | 16 ++++++------- devtools/test/chunkgrphrcipTransmissionTest.m | 8 +++---- devtools/test/chunkgrphregionTest.m | 16 ++++++------- devtools/test/chunkrgrphOpdimTest.m | 6 ++--- 11 files changed, 59 insertions(+), 59 deletions(-) diff --git a/chunkie/@chunkgraph/chunkgraph.m b/chunkie/@chunkgraph/chunkgraph.m index fd48d34..42c0531 100644 --- a/chunkie/@chunkgraph/chunkgraph.m +++ b/chunkie/@chunkgraph/chunkgraph.m @@ -8,7 +8,7 @@ % properties(SetAccess=public) verts - verts2edge + edge2verts echnks regions vstruc @@ -25,7 +25,7 @@ end methods - function obj = chunkgraph(verts,verts2edge,fchnks,cparams) + function obj = chunkgraph(verts,edge2verts,fchnks,cparams) if (nargin == 0) return end @@ -33,7 +33,7 @@ return end obj.verts = verts; - obj.verts2edge = verts2edge; + obj.edge2verts = edge2verts; obj.echnks = chunker.empty; if (nargin < 4) @@ -66,15 +66,15 @@ pref.nchmax = 10000; pref.k = 16; - if (size(verts,2) ~= size(verts2edge,2)) + if (size(verts,2) ~= size(edge2verts,2)) error('Incompatible vertex and edge sizes'); end echnks = chunker.empty(); - for i=1:size(verts2edge,1) + for i=1:size(edge2verts,1) if (numel(fchnks) Date: Tue, 31 Oct 2023 13:16:00 -0400 Subject: [PATCH 17/23] small changes to remove print statements --- chunkie/mergeregions.m | 7 ------- chunkie/regioninside.m | 2 -- devtools/test/chunkgrphregionTest.m | 1 - devtools/test/refine_trefinementTest.m | 7 ------- 4 files changed, 17 deletions(-) diff --git a/chunkie/mergeregions.m b/chunkie/mergeregions.m index c484742..110e8b9 100644 --- a/chunkie/mergeregions.m +++ b/chunkie/mergeregions.m @@ -9,8 +9,6 @@ irgn = 0; for ii=2:numel(rgn1) nin = pointinregion(cgrph,rgn1{ii},v2); - disp("first inclusion:") - nin if (nin > 0 && mod(nin,2)==1) if (irgn ~= 0) disp("Warning: an unsupported geometry error has occurred"); @@ -35,8 +33,6 @@ irgn = 0; for ii=2:numel(rgn2) nin = pointinregion(cgrph,rgn2{ii},v1); - disp("second inclusion:") - nin if (nin > 0 && mod(nin,2)==1) if (irgn ~= 0) disp("Warning: an unsupported geometry error has occurred"); @@ -46,8 +42,6 @@ end if (irgn ~= 0) - disp("here") - irgn rgnout = rgn2; rgnout = [rgnout,rgn1(2:end)]; rgnout{irgn} = [rgnout{irgn},rgn1{1}]; @@ -55,7 +49,6 @@ end if (irgn1==0 && irgn==0) - disp("here also") rgnout = rgn1; rgnout = [rgnout,rgn2(2:end)]; rgnout{1} = [rgnout{1},rgn2{1}]; diff --git a/chunkie/regioninside.m b/chunkie/regioninside.m index db32ab0..a4e5351 100644 --- a/chunkie/regioninside.m +++ b/chunkie/regioninside.m @@ -6,8 +6,6 @@ irgn = 0; for ii=2:numel(rgn1) nin = pointinregion(cgrph,rgn1{ii},v2); - disp("first inclusion:") - nin if (nin > 0 && mod(nin,2)==1) if (irgn ~= 0) disp("Warning: an unsupported geometry error has occurred"); diff --git a/devtools/test/chunkgrphregionTest.m b/devtools/test/chunkgrphregionTest.m index 0ede369..eadd8b6 100644 --- a/devtools/test/chunkgrphregionTest.m +++ b/devtools/test/chunkgrphregionTest.m @@ -55,7 +55,6 @@ [cgrph] = chunkgraph(verts,verts2edge,fchnks,prefs); vstruc = procverts(cgrph); -%rgns = findregions(cgrph); cgrph = balance(cgrph); % rgns = cgrph.regions; diff --git a/devtools/test/refine_trefinementTest.m b/devtools/test/refine_trefinementTest.m index 9b8bdf1..fde86aa 100644 --- a/devtools/test/refine_trefinementTest.m +++ b/devtools/test/refine_trefinementTest.m @@ -43,17 +43,13 @@ h2 = chnkr.h(i2); end if (hself > 2*h1) - fprintf('oh no! 1 %d\n',i) happy = false; end if (hself > 2*h2) - fprintf('oh no! 2 %d\n',i) happy = false; end end -fprintf('happy? %s\n',mat2str(happy)) - % enforce level restriction using refine code with % specific options @@ -78,13 +74,10 @@ h2 = chnkr.h(i2); end if (hself > 2*h1) - fprintf('oh no! 1 %d\n',i) happy = false; end if (hself > 2*h2) - fprintf('oh no! 2 %d\n',i) happy = false; end end -fprintf('happy? %s\n',mat2str(happy)) From 97c003b7420679eaf41a001b88677104919b14d5 Mon Sep 17 00:00:00 2001 From: Manas Rachh Date: Tue, 31 Oct 2023 13:43:39 -0400 Subject: [PATCH 18/23] adding readthedocs yaml --- .readthedocs.yaml | 32 ++++++++++++++++++++++++++++++++ 1 file changed, 32 insertions(+) create mode 100644 .readthedocs.yaml diff --git a/.readthedocs.yaml b/.readthedocs.yaml new file mode 100644 index 0000000..d69d7c2 --- /dev/null +++ b/.readthedocs.yaml @@ -0,0 +1,32 @@ +# .readthedocs.yaml +# Read the Docs configuration file +# See https://docs.readthedocs.io/en/stable/config-file/v2.html for details + +# Required +version: 2 + +# Set the OS, Python version and other tools you might need +build: + os: ubuntu-22.04 + tools: + python: "3.12" + # You can also specify other tool versions: + # nodejs: "19" + # rust: "1.64" + # golang: "1.19" + +# Build documentation in the "docs/" directory with Sphinx +sphinx: + configuration: docs/conf.py + +# Optionally build your docs in additional formats such as PDF and ePub +# formats: +# - pdf +# - epub + +# Optional but recommended, declare the Python requirements required +# to build your documentation +# See https://docs.readthedocs.io/en/stable/guides/reproducible-builds.html +# python: +# install: +# - requirements: docs/requirements.txt From 0146ec39317ed0585a670cda3b8cfe8ddd6cf01a Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Tue, 31 Oct 2023 13:44:08 -0400 Subject: [PATCH 19/23] bug fix in transmission helper --- chunkie/+chnk/+helm2d/transmission_helper.m | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/chunkie/+chnk/+helm2d/transmission_helper.m b/chunkie/+chnk/+helm2d/transmission_helper.m index 553dd34..b199e36 100644 --- a/chunkie/+chnk/+helm2d/transmission_helper.m +++ b/chunkie/+chnk/+helm2d/transmission_helper.m @@ -151,7 +151,7 @@ c1 = coefs(d1); c2 = coefs(d2); ind1 = sum(nchs(1:i-1))*ngl*2+(1:2:2*nchs(i)*ngl); - ind2 = sum(nchs(1:i-1))*ngl*2+(1:2:2*nchs(i)*ngl); + ind2 = sum(nchs(1:i-1))*ngl*2+(2:2:2*nchs(i)*ngl); targnorm = chnkrs(i).n; nx = targnorm(1,:); nx = nx(:); ny = targnorm(2,:); ny = ny(:); From 6ea419feb0f7a24cc7dd5f1ebebbac4617a6955c Mon Sep 17 00:00:00 2001 From: Manas Rachh Date: Tue, 31 Oct 2023 13:46:45 -0400 Subject: [PATCH 20/23] updating conf --- docs/conf.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/conf.py b/docs/conf.py index aa90e8e..6f2189e 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -83,7 +83,7 @@ # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # -html_theme = 'sphinx_rtd_theme' +html_theme = 'sphinx-rtd-theme' # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the From af21c7c6a6c43aac40fe71ee74e65cab9f5a18f9 Mon Sep 17 00:00:00 2001 From: Manas Rachh Date: Tue, 31 Oct 2023 13:53:09 -0400 Subject: [PATCH 21/23] trying to address themes issue in read the docs --- .readthedocs.yaml | 6 +++--- docs/conf.py | 2 +- docs/requirements.txt | 1 + 3 files changed, 5 insertions(+), 4 deletions(-) create mode 100644 docs/requirements.txt diff --git a/.readthedocs.yaml b/.readthedocs.yaml index d69d7c2..974aa27 100644 --- a/.readthedocs.yaml +++ b/.readthedocs.yaml @@ -27,6 +27,6 @@ sphinx: # Optional but recommended, declare the Python requirements required # to build your documentation # See https://docs.readthedocs.io/en/stable/guides/reproducible-builds.html -# python: -# install: -# - requirements: docs/requirements.txt + python: + install: + - requirements: docs/requirements.txt diff --git a/docs/conf.py b/docs/conf.py index 6f2189e..aa90e8e 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -83,7 +83,7 @@ # The theme to use for HTML and HTML Help pages. See the documentation for # a list of builtin themes. # -html_theme = 'sphinx-rtd-theme' +html_theme = 'sphinx_rtd_theme' # Theme options are theme-specific and customize the look and feel of a theme # further. For a list of options available for each theme, see the diff --git a/docs/requirements.txt b/docs/requirements.txt new file mode 100644 index 0000000..483a4e9 --- /dev/null +++ b/docs/requirements.txt @@ -0,0 +1 @@ +sphinx_rtd_theme From eb4b8bcf8272cf1068536b50e7c9f62483f4e940 Mon Sep 17 00:00:00 2001 From: Manas Rachh Date: Tue, 31 Oct 2023 13:54:49 -0400 Subject: [PATCH 22/23] trying to fix yaml --- .readthedocs.yaml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.readthedocs.yaml b/.readthedocs.yaml index 974aa27..8325091 100644 --- a/.readthedocs.yaml +++ b/.readthedocs.yaml @@ -27,6 +27,6 @@ sphinx: # Optional but recommended, declare the Python requirements required # to build your documentation # See https://docs.readthedocs.io/en/stable/guides/reproducible-builds.html - python: - install: +python: + install: - requirements: docs/requirements.txt From c8ec5da46832483838d38f816aa6f8f8c48518f1 Mon Sep 17 00:00:00 2001 From: Travis Askham Date: Tue, 31 Oct 2023 14:08:17 -0400 Subject: [PATCH 23/23] updates to install instructions --- docs/getchunkie.rst | 51 ++++++++++++++++++++++++++++++++++++++------- 1 file changed, 43 insertions(+), 8 deletions(-) diff --git a/docs/getchunkie.rst b/docs/getchunkie.rst index 73a7267..82d2c23 100644 --- a/docs/getchunkie.rst +++ b/docs/getchunkie.rst @@ -1,18 +1,53 @@ Get Chunkie ============ -Downloads -------------- - -- Latest release: ' - - Installation Instructions -------------------------- +Clone the repository with the submodules + +.. code:: bash + + git clone --recurse-submodules https://github.com/fastalgorithms/chunkie.git + +and run startup.m in the install directory. +This will download the FLAM and fmm2d submodules, include FLAM in +the matlab path, and generate the fmm2d mex file if a fortran compiler +exists. + Troubleshooting ----------------- -For some systems, the standard installation of the fmm2d library -results in errors. tktktktktk +- The fmm2d mex installation is currently not supported on Windows, to + complete the mex installation, follow instructions on the `fmm2d documentation `_ +- fmm2d mex installation depends on gfortran. In case a compiler is not + found, the installation will be skipped. To install dependencies follow the procedure below based on your OS + + * MacOS + + Get xcode, command line tools by running + + .. code:: bash + + xcode-select --install + + Then install Homebrew from https://brew.sh, and finally install gfortran using + + .. code:: bash + + brew install gcc + + * Ubuntu linux + + .. code:: bash + + sudo apt-get install make build-essential gfortran + + * Fedora/centOS linux + + .. code:: bash + + sudo yum install make gcc gcc-c++ gcc-gfortran libgomp + +- If installing without submodules, chunkie depends on `FLAM `_, and optionally on the `fmm2d `_ repository. Parts of the library will not function without FLAM and its subdirectories included in the matlab path.