Message Boards Message Boards

0
|
2919 Views
|
3 Replies
|
0 Total Likes
View groups...
Share
Share this post:
GROUPS:

Reap Sow and StepMonitor with FEM in Mathematica

Hello,

Can anyone help me figure out how to use Reap, Sow and StepMonitor with NDSolve applications using finite element module?

Thanks in advance.

Housam

KFUPM, KSA

POSTED BY: Housam Binous
3 Replies

Doesn't seem to work.

In[5]:= Needs["NDSolve`FEM`"]

In[8]:= \[CapitalOmega] = 
  ImplicitRegion[! ((x - 5)^2 + (y - 5)^2 <= 3^2), {{x, 0, 5}, {y, 0, 
     10}}];

In[11]:= op = -Laplacian[u[x, y], {x, y}] - 20;

In[9]:= Subscript[\[CapitalGamma], 
  D] = {DirichletCondition[u[x, y] == 0, x == 0 && 8 <= y <= 10],
   DirichletCondition[u[x, y] == 100, (x - 5)^2 + (y - 5)^2 == 3^2]};

In[13]:= res = 
 Reap @ NDSolveValue[{op == 
     0, {DirichletCondition[u[x, y] == 0, x == 0 && 8 <= y <= 10], 
     DirichletCondition[
      u[x, y] == 100, (-5 + x)^2 + (-5 + y)^2 == 9]}}, 
   u, {x, y} \[Element] 
    ImplicitRegion[(-5 + x)^2 + (-5 + y)^2 > 9 && 0 <= x <= 5 && 
      0 <= y <= 10, {x, y}], EvaluationMonitor :> Sow[{x, y, u[x, y]}]]

Out[13]= {InterpolatingFunction[{{0., 5.}, {0., 10.}}, <>], {}}
POSTED BY: Frank Kampas

Dear Frank,

I know this. Can you do something similar with NDSolve for PDEs using Mathematica's finite element package?

Thanks much,

Housam

POSTED BY: Housam Binous

Here's how to do it with a one-dimensional problem.

In[1]:= res = 
  Reap[NDSolve[{y'[t] == y[t], y[0] == 1}, y, {t, 0, 1}, 
    EvaluationMonitor :> Sow[y[t]]]];

In[2]:= res

Out[2]= {{{y -> InterpolatingFunction[{{0., 1.}}, <>]}}, {{1., 
   1.00009, 1.00009, 1.00018, 1.00018, 1.00471, 1.00471, 1.00926, 
   1.00926, 1.01383, 1.01383, 1.03331, 1.03331, 1.02801, 1.02801, 
   1.0424, 1.0424, 1.05699, 1.05699, 1.07178, 1.07178, 1.10199, 
   1.10199, 1.13305, 1.13305, 1.16498, 1.16498, 1.19781, 1.19781, 
   1.23157, 1.23157, 1.31583, 1.31583, 1.40584, 1.40584, 1.50202, 
   1.50202, 1.60477, 1.60477, 1.71456, 1.71456, 1.83185, 1.83185, 
   2.02451, 2.02451, 2.23743, 2.23743, 2.46616, 2.46616, 2.71828, 
   2.71828}}}
POSTED BY: Frank Kampas
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract