Describing a pde model geometry that can have multiple domains

Question

Andrei Cheplakov 2023-12-6

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https://ww2.mathworks.cn/matlabcentral/answers/2057149-describing-a-pde-model-geometry-that-can-have-multiple-domains

回答： Jiexian Ma 2025-4-5

Let's say I have a certain number of polygons (given by the coordinates of their points), which make up a geometry in which I want to solve a pde. The number of polygons, as well as their size, can be changed:

% Height and width of polygons
size_x = 0.5;
size_y = 3;
% Number of polygons
Npoly = 5;
figure;
hold on;
axis equal;
for i = 1:Npoly
    % Getting coordinates of current polygon's points
    p1_x(i) = (i-1)*size_x;
    p1_y(i) = 0;
    p2_x(i) = size_y + (i-1)*size_x;
    p2_y(i) = size_y;
    p3_x(i) = size_y + size_x + (i-1)*size_x;
    p3_y(i) = size_y;
    p4_x(i) = size_x + (i-1)*size_x;
    p4_y(i) = 0;
    points = [p1_x(i),p1_y(i); p2_x(i),p2_y(i); p3_x(i),p3_y(i); p4_x(i),p4_y(i)];
    % Plotting polygon
    pg = polyshape(points(:,1),points(:,2));
    plot(pg); 
end

Each polygon represents a separate domain, and some constant present in the pde can vary between them, so I need a way of labeling parts of the geometry.

Is it possible to somehow convert these polygons into a model geometry, so that they form separate domains?

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Andrei Cheplakov 2023-12-6

编辑：Andrei Cheplakov 2023-12-6

I actually figured out how to do this. I used the cgs modelling method, and combined a base rectangle with the coordinates that I got for each polygon. I changed the code slightly, so that there is a spacing between consecutive polygons, and this is what I ended up with: