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traction matlab demo #52

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merged 2 commits into from
Apr 12, 2024
Merged

traction matlab demo #52

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f0430e7
add traction extraction demo to stfmm3dPerfTest.m
ahbarnett Apr 12, 2024
3ce46b8
Merge branch 'flatironinstitute:master' into master
ahbarnett Apr 12, 2024
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2 changes: 1 addition & 1 deletion matlab/Contents.m
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Original file line number Diff line number Diff line change
Expand Up @@ -16,7 +16,7 @@
% hfmm3dTest
% emfmm3dTest
% stfmm3dTest
% stfmm3dPerfTest
% stfmm3dPerfTest - demo and math test for stokeslet & stresslet, traction
%
% For examples of use see:
% lfmm3d_example
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43 changes: 39 additions & 4 deletions matlab/stfmm3dPerfTest.m
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Original file line number Diff line number Diff line change
@@ -1,11 +1,13 @@
disp("Perf and math test matlab driver for FMM3D/Stokes")
disp("Source to target, stokeslet+stresslet (1-vec), vel pot only...");
% Barnett 8/4/23
% Barnett 8/4/23. Added traction output test, 4/12/24.

clear
ns = 100000;
nt = 100000;
eps = 1e-3;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp("Source to target, stokeslet+stresslet (1-vec), vel pot only...");
ifstrs = 1; % include stresslets?
ifppreg = 0; % no eval at sources
ifppregtarg = 1; % just vel out
Expand All @@ -24,7 +26,7 @@
t = toc;
fprintf("%d to %d points, eps=%.3g, done in %.3g s (%.3g tot pts/sec)\n",ns,nt,eps,t,(ns+nt)/t)
u = U.pottarg;
i = randi(nt); % which targ
i = randi(nt); % which targ to check
fprintf("velpot targ(i=%d) =\n",i);
disp(u(:,i))

Expand All @@ -42,6 +44,39 @@
end
end
ui = 0.5 * ui; % FMM3D is 1/4pi off from true 1/8pi prefactor
fprintf("rel err vs direct at ith targ: %.3g\n",norm(u(:,i)-ui)/norm(ui))
fprintf("rel err vs direct at ith targ: %.3g\n\n",norm(u(:,i)-ui)/norm(ui))


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp("Stokeslet sources to targets: compute vel pot, traction at oriented targs...");
% just give the changes from the above setup...
ifppregtarg = 3; % request everything
srcinfo = rmfield(srcinfo,{'strslet','strsvec'});
targnor = rand(3,nt); % normal vectors for targets (eg, surface normals)

tic;
U = stfmm3d(eps,srcinfo,ifppreg,targ,ifppregtarg);
t = toc;
fprintf("%d to %d points with u,p,gradu: done in %.3g s (%.3g tot pts/sec)\n",ns,nt,t,(ns+nt)/t)
p = U.pretarg; % pressure (1*ntarg)
gradu = U.gradtarg; % grad vel (3*3*ntarg)
shearstress = gradu + permute(gradu,[2 1 3]); % gradu + gradu^T
% stress sigma = -pI + mu*(gradu+gradu^T), then T = sigma.n We assume mu=1.
T = -(ones(3,1)*p).*targnor + squeeze(sum(shearstress .* reshape(kron(ones(3,1),targnor),3,3,nt),1)); % compute all tractions (painful tensor contraction in matlab)
i = randi(nt); % which targ to check
%fprintf("targ(i=%d): p=%.15g, gradu = \n",i,p(i)); disp(gradu(:,:,i))
fprintf("targ(i=%d) traction T = \n",i);
disp(T(:,i))

% check T (target tractions) vs direct formula
Ti = zeros(3,1);
nori = targnor(:,i);
for j=1:ns
R = targ(:,i) - srcinfo.sources(:,j); % x-y with std sign (targ-src).
r = sqrt(sum(R.^2)); % dist
f = srcinfo.stoklet(:,j); % strength
Ti = Ti - (3/(4*pi))*(1/r^5)*R*dot(nori,R)*dot(f,R); % true T_{ijk} n_j f_k
end
Ti = Ti * (4*pi); % FMM3D has 1/4pi missing in prefactor
fprintf("rel err vs direct at ith targ: %.3g\n",norm(T(:,i)-Ti)/norm(Ti))

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