I'm trying to solve heat governing equation using finite element method but i'm having error that I can't figure it out.

Can anybody help me to figure out this,

Im trying to solve this equation

This is the error I am getting.

Index exceeds the number of array elements. Index must not exceed 9.

Error in decsg (line 172)

a=atan2(diff(gdc([3+gdc(2):2+2*gdc(2),3+gdc(2)])),...

Error in FEM_Temp (line 14)

g = decsg(gm,sf,ns);

This in my code:

FEM_Temp

Index exceeds the number of array elements. Index must not exceed 9.

Error in decsg (line 172)
a=atan2(diff(gdc([3+gdc(2):2+2*gdc(2),3+gdc(2)])),...

Error in solution>FEM_Temp (line 15)
g = decsg(gm,sf,ns);

function FEM_Temp
% variables
rho = 1234.2;
Cp = 2.195;
k = 0.054;
% Geometry & Mesh
model = createpde(3);
R1 = [3 4 -1 1 0 1 0 0 0]';
R2 = [3 4 0 1 0 1 0 0 0]';
gm = [R1 R2];
sf = 'R1+R2';
ns = (char('R1','R2'))';
g = decsg(gm,sf,ns);
geometryFromEdges(model,g);
hmax = 0.1; % Max element size
generateMesh(model,'Hmax',hmax);
% initial conditions
T0 = 100*ones(size(model.Mesh.Nodes,1), 1);
T0(abs(model.Mesh.Nodes(:,1)-0.5) < 0.1 & abs(model.Mesh.Nodes(:,2)-0.5) < 0.1 & abs(model.Mesh.Nodes(:,3)-0.5) < 0.1) = 200;
%boundary conditions
specifyCoefficients(model,'m',0,'d',1,'c',k/(rho*Cp),'a',0,'f',0);
applyBoundaryCondition(model,'face',[1,2],'h',@h_bc);
applyBoundaryCondition(model,'face',3,'q',-10);
specifyCoefficients(model,'Face',3,'h',0,'q',-10);
% Define boundary condition functions
    function [pl,ql,pr,qr] = h_bc(~, ~, state)
        pl = state.ux;
        ql = 0;
        pr = 0;
        qr = 1;
    end
% time-dependent set up
tlist = linspace(0,10,101);
result = solvepde(model,tlist,'InitialConditions',T0);
% Plot Temp vs Time
u = result.NodalSolution(:, end);
pdeplot3D(model.Mesh.Nodes,model.Mesh.Elements,'ColorMapData',u,'FaceAlpha',0.5);
colorbar;
xlabel('x');
ylabel('y');
zlabel('z');
title('Temperature Distribution');
end % Main function end

Answer 1

[Walter Roberson]

decsg documentation says

For a rectangle, the first row contains 3, and the second row contains 4. The next four rows contain the x-coordinates of the starting points of the edges, and the four rows after that contain the y-coordinates of the starting points of the edges.

That is a total of 10 rows but you are only passing 9 rows

[Stark Volt]

Thanks for reply so I am only allowed to pass 9 rows?

[Walter Roberson]

No the problem is that you did pass 9 rows but those rows encode rectangles which require 10 rows to encode.

[Stark Volt]

Thanks I will try and modify to see if it will work thanks