MATLAB: Interpolation of the results from the PDE toolbox and the spatial differentiation of the solution

interpolation of fea resultspde toolboxspatial derivative

Hello,

I am trying to solve a PDE within a rectangular region with the Matlab PDE toolbox. I am facing two problems:

(1) As shown in the example, I can solve the PDE with the commands:

R = solvepde(model);

u = R.NodalSolution;

figure

pdeplot(model,'XYData',u,'Contour','on','ColorMap','jet')

However, I want the solution to be evaluated at the regular grid points, not at the nodes. How can I get the value of u at specific (x,y) points?

(2) I would also like to evaluate the spatial differentiation of the solution u, that is, I want to calculate du/dx and du/dy at the regular grid points. I can do it numerically, but I just want to do all the things directly from Matlab. Is there any command that can help me?

Thank you very much.

Khalid

Best Answer

You can do this using interpolateSolution and evaluateGradients.

Regards,

Ravi

Related Solutions

MATLAB: Refine mesh in PDEModel

You cannot refine a mesh using a PDEModel. You have to import the geometry (I assume that you did that before trying to create a mesh) and then call generateMesh using an appropriate value of Hmax. If you need more nodes, just call generateMesh again using a smaller value of Hmax.

Alan Weiss

MATLAB mathematical toolbox documentation

MATLAB: EvaluateGradient missing from pde toolbox

Hi Heidi,

You need to have a results object in the workspace to access evaliuateGradient on the MATLAB path. Run any PDEModel based example and then you will be able to access it.

evaliuateGradient is a method so you won't be able access it without a resutls object. Copy and paste the following code.

   %Create a PDEModel, import geometry, and specify coefficients.
      N = 1; % single PDE
      pdem = createpde(N);
      g = importGeometry(pdem,'Block.stl');
      c = 1;
      a = 0;
      f = 0.1;
      specifyCoefficients(pdem,'m',0,'d',0,'c',c,'a',a,'f',f);
 
      %Apply boundary conditions and generate the mesh.
      applyBoundaryCondition(pdem,'dirichlet','Face',1:4,'u',0);
      applyBoundaryCondition(pdem,'neumann','Face',6,'g',-1);
      applyBoundaryCondition(pdem,'neumann','Face',5,'g',1);
 
      generateMesh(pdem);
 
      %Solve the PDE.
      R = solvepde(pdem);
 
      %Define a grid of points representing the mid-plane of the plate.
      xp = 0:2:100; yp = 0:2:50;
      [XX, ZZ] = meshgrid(xp,yp);
      YY = 2*ones(size(XX));
 
      %Evaluate gradients of the solution on the mid-plane grid.
      [dudx, dudy, dudz] = evaluateGradient(R,XX,YY,ZZ);
 
      %Reshape the gradients to visualize using the MATLAB surf function.
      dudxres = reshape(dudx,size(XX));
      dudyres = reshape(dudy,size(XX));
      dudzres = reshape(dudz,size(XX));
 
      %Visualize the gradients of solution on the mid-plane.
      figure
      subplot(1,3,1)
      surf(XX,ZZ,dudxres)
      xlabel('x'); ylabel('y'); zlabel('du/dx');
 
      subplot(1,3,2)
      surf(XX,ZZ,dudyres)
      xlabel('x'); ylabel('y'); zlabel('du/dy');
 
      subplot(1,3,3)
      surf(XX,ZZ,dudzres)
      xlabel('x'); ylabel('y'); zlabel('du/dz');