Add documentation for math function

user/preprocess/input.md

@@ -116,6 +116,11 @@ The CB-Geo MPM code uses a `JSON` file for input configuration.
       "type": "Linear",
       "xvalues": [0.0, 0.5, 1.0],
       "fxvalues": [0.0, 1.0, 1.0]
+    },
+    {
+      "id": 1,
+      "type": "Linear",
+      "file": "math-function.csv"
     }
   ],
   "analysis": {
@@ -371,31 +376,10 @@ A load without a math function will be applied as a static load. Use math functi
 
 Both `concentrated_nodal_forces` and `particle_surfacce_traction` use [`entity_sets`](./entity_sets) to apply forces on a set of nodes and particles. The loading can be time-varying. The time-variation of the load can be specified using a math function. Setting the `nset_id` or `pset_id` to `-1` will apply the loading to all the nodes and particles. 
 
-### Math functions
-
-Math functions are useful to define how a certain load varies with time. A typical math function is shown below.
-
-```
-  "math_functions": [
-    {
-      "id": 0,
-      "type": "Linear",
-      "xvalues": [0.0, 0.5, 1.0, 1.5],
-      "fxvalues": [0.0, 1.0, 1.0, 0.0],
-    }
-  ]
-```
-
-This is a linear function with x and corresponding f(x) values. The function varies as shown in the figure. If used with a traction, the value of traction at different times will be computed as the defined math function.
-
-![x_fx](x_fx.png)
-
-
 ### ASCII loading conditions
 > Warning: ASCII loading conditions do not support math functions
 
-Loading conditions on the nodes can also be specified through an ASCII file. The JSON configuration for the boundary
-condition is:
+Loading conditions on the nodes can also be specified through an ASCII file. The JSON configuration for the loading condition is:
 
 ```
   "external_loading_conditions": {
@@ -562,3 +546,54 @@ where,
 
 `f_i` is the friction coefficient.
 
+## Math functions
+
+Math functions are useful to define how a certain load varies with time. A typical math function is shown below.
+
+```
+  "math_functions": [
+    {
+      "id": 0,
+      "type": "Linear",
+      "xvalues": [0.0, 0.5, 1.0, 1.5],
+      "fxvalues": [0.0, 1.0, 1.0, 0.0],
+    }
+  ]
+```
+
+This is a linear function with x and corresponding f(x) values. The function varies as shown in the figure. If used with a traction, the value of traction at different times will be computed as the defined math function.
+
+![x_fx](x_fx.png)
+
+### CSV Math Functions
+Math functions can also be specified through a CSV file, and this is useful when they are rather long such as math functions used to define time history of a dynamic earthquake ground motion. The JSON configuration for the math function is:
+
+```
+  "math_functions": [
+    {
+      "id": 1,
+      "type": "Linear",
+      "file": "math-function.csv"
+    }
+  ]
+```
+
+Math function can be specified in the following format:
+
+```
+#xvalue, fxvalue
+x_0,  fx_0, 
+x_1,  fx_1, 
+...,   ...,
+...,   ..., 
+x_i,  fx_i, 
+...,   ...,
+...,   ...,
+x_n,  fx_n 
+```
+
+where, 
+
+`x_i` is the independent varirable x,
+
+`fx_i` is the dependent variable f(x).