Error: Invalid geometry detected. Edges overlap or intersect at non-end points. for expanding circular subdomains inside larger circle

I have a code that creates a circle with radius 1 and a center at (0,0) at the first iteration. At the 2nd iteration, 10 small circles with radius 0.01 form at random coordinates inside the circle and expand by 0.01 with each following iteration.

Here's my code:

for jj = 1:100
    % take nodes from step 1 and apply to step 2 to find coordinates
    if jj == 2
        NN = model_temp.Mesh.Nodes; XX=NN(1,:)'; YY=NN(2,:)';
    end

      % Create the PDE Model with a single dependent variable 
          numberOfPDE = 1;
          model_temp = createpde(numberOfPDE);
      %%%%%%%%%%%%%%%%%%%%%%%%%Geometry %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      if jj == 1
          gdm = [1 0 0 1]';
          ns = ('C1');
          sf = 'C1';
          [g,bt] = decsg(gdm,sf,ns');
      elseif jj > 1
          if jj == 2
              r = 1;
              c_coords = [0 0]';
              ncirc = 10; % number of smaller circles
              innerRs = ones(1,ncirc)*0.01; % starting radii of inner circles
              r = [r innerRs]; % radii of circles
              NewC = [];
              while size(NewC,2) < ncirc
                  C = randsample(length(NN),1); loc = NN(:,C); % finds random nodes from first mesh to act as center  
                    % coordinates for inner circles
                  NewC = [NewC loc];
              end
              c_coords = [c_coords NewC];
          else
              r(2:end) = r(2:end) + 0.01; % at all other iterations, increase inner radii
          end
              gdm = [ones(1,length(r));c_coords;r];
              ns = [repmat('C',length(r),1),num2str((1:length(r))', '%-d')];
              sf = [ns,repmat('+',length(r),1)]';
              sf = sf(:); sf(end) = [];sf = sf';
              srt = find(sf == 'C'); sf2 = sf(srt(2):end);
              sf = ['(',sf,') - ((',sf2,')-C1)'];
              [g,bt] = decsg(gdm,sf,ns');

      end

      geometryFromEdges(model_temp,g);
      Hmax = 0.035;
      msh = generateMesh(model_temp,'Hmax',Hmax);
      pdeplot(model_temp);
  end

Since I want to keep the coordinates random, each time I run the code I get different figures. Sometimes when I run it I get the error: "Invalid geometry detected. Edges overlap or intersect at non-end points." I don't know if it's a problem with my code because sometimes when I run it, I don't get any errors.

I read online that this could be caused by a bug in the PDE toolbox. What can I do to avoid this problem?

Answer 1

[Jatin Waghela]

You may refer to the similar issue discussed at the below link:

https://www.mathworks.com/matlabcentral/answers/328255-how-to-fix-an-error-when-trying-to-create-a-geometry-for-pde

Use geometry functions to define the geometry as stated in the documentation:

https://www.mathworks.com/help/pde/ug/create-geometry-using-a-geometry-function.html

Additional suggestions are found in the following post:

https://www.mathworks.com/matlabcentral/answers/327922-how-to-use-the-pde-toolbox-combined-with-the-script