2-D Laplace Equation

How would I be able to set up a matlab code for a 2-D Laplace for hydraulic head. The shape is a polygon. Thanks!

[Torsten]

This will be a hard job for an arbitrary polygonal region.

Use the PDE Toolbox instead of trying to code it on your own.

Answer 1

[SAI SRUJAN]

Hi Abigail,

I understand that you are trying to set up a MATLAB code for a 2D Laplace for hydraulic head.

Please follow the below code sample to proceed further which uses the functions of PDE Toolbox,

% This is an example for a simple square; you'll need to adjust it for your polygon
gd = [3; 4; 0; 1; 1; 0; 0; 0; 1; 1]; 

% Step 2: Create PDE model
model = createpde(1);

% Step 3: Assign geometry to the model
geometryFromEdges(model,gd);

% Step 4: Set boundary conditions (example)
applyBoundaryCondition(model,'dirichlet','Edge',1:model.Geometry.NumEdges,'u',0);

generateMesh(model);
result = solvepde(model);
figure;
pdeplot(model,'XYData',result.NodalSolution);
title('Hydraulic Head Distribution');

Please refer to the following MATLAB Central Answers thread, which discusses solving 2D Laplace equations using boundary value problem (BVP) solvers.

https://www.mathworks.com/matlabcentral/answers/455372-using-bvp-solver-to-solve-2-d-laplace-s-equation

For a comprehensive understanding of the 'solvepde' function in MATLAB, please refer to the following documentation.

https://www.mathworks.com/help/pde/ug/pde.pdemodel.solvepde.html

I hope this helps!