What is the largest number of DOFs that MATLAB pdetool can solve without running into memory issues?

What limitations are there on the size of the problem that MATLAB can solve? Is there a way to parallelize the problem within the MATLAB environment (either with multiple processors or GPUs)?

Answer 1

[Alan Weiss]

In 2-D you can have a pretty large problem. Are you running into issues?

In 3-D the solution can run into memory issues. It is easy for 3-D meshes to have many more elements than 2-D meshes.

No, there is no built-in parallel support in PDE Toolbox.

Alan Weiss

MATLAB mathematical toolbox documentation

[Brian]

I am not running into issues at this time, but having coded my own FE solver for 2D square plane-strain elements using sparse matrices in MATLAB, I noticed that around roughly 50,000 DOFs I was running into memory issues. It seems like the same issue would occur if I attempted a similar sized problem using the pdetool.

Brian

[Alan Weiss]

I just tried running a simple PDE solution on a triangular mesh with over 100,000 elements and over 50,000 nodes. The mesh took a while to create (about a minute), but the problem solution took less than a second.

model = createpde;
geometryFromEdges(model,@lshapeg);
c = 1;
a = 0;
f = 1;
applyBoundaryCondition(model,'Edge',1:model.Geometry.NumEdges,'u',0);
tic
generateMesh(model,'Hmax',1e-2);
toc
tic
u = assempde(model,c,a,f);
toc

Alan Weiss

MATLAB mathematical toolbox documentation

[Alan Weiss]

By the way, the newer mesher version works much faster:

tic
generateMesh(model,'Hmax',1e-2,'MesherVersion','R2013a');
toc

For me this was nearly ten times faster, just a few seconds to generate the mesh.

Alan Weiss

MATLAB mathematical toolbox documentation