How I introduce a matrix form of c coefficient in PDE equation using solvepde matlab command

Hello,

please how I introduce the c coeffecient which is has a matrix form:

c = [x-y, 0; 1, x.^2]

using "specifyCoefficients" and "solvepde" matlab command?

With best regards

I try this code

%======================================

numberOfPDE = 1;

model = createpde(numberOfPDE);

r1 = [3,4,0,0,0.5*10^-6,0.5*10^-6,-160*10^-9,-1.16*10^-6,-1.16*10^-6,-160*10^-9];

r2 = [3,4,0,0,0.5*10^-6,0.5*10^-6,0,-160*10^-9,-160*10^-9,0];

gdm = [r1; r2]';

g = decsg(gdm,'R1+R2',['R1'; 'R2']');

geometryFromEdges(model,g);

C = @(location,~)[location.x-location.y,0;1,location.x.^2];

F=@(location,~)location.x;

specifyCoefficientsspecifyCoefficients(model,'m',0,'d',0,'c',C,'a',0,'f',F);

msh = generateMesh(model,'Hmax',0.02,'GeometricOrder','linear','Jiggle','on');

pdeplot(model);

[p,e,t] = meshToPet(msh);

results = solvepde(model)

%==================================================================

and I obtain the error message:

Error using formGlobalKF2D

Coefficient evaluation function, "@(location,~)[location.x-location.y,0;1,location.x.^2]", was requested to calculate

coefficients at 1 locations so should have returned a matrix with 1 columns. Instead it returned a matrix with 2 columns.

Answer 1

[Ravi Kumar]

Output of c coefficient function should be a matrix or column vector of appropriate size, where the number of columns corresponds to spatial locations as provided by location.x and location.y. Try this:

C = @(location,~)[location.x-location.y; ...
                    ones(size(location.x));...
                    zeros(size(location.x));...
                             location.x.^2];