PDE Parabolic coefficient

Hi !

This is the first time I use matlab, so I have a bad level.

Parabolic solver has this form:

u1=parabolic(u0,tlist,b,p,e,t,c,a,f,d)

It is said on this page (<http://www-rohan.sdsu.edu/doc/matlab/toolbox/pde/assempde.html>) that "*c*" coefficient can be a 2by2 matrix.

Here is my little code :

[p,e,t]=initmesh('squareg'); 
[p,e,t]=refinemesh('squareg',p,e,t); 
u0=zeros(size(p,2),1); 
ix=find(sqrt(p(1,:).^2+p(2,:).^2)<0.4); 
u0(ix)=ones(size(ix)); 
tlist=linspace(0,0.1,20); 
c=[1 2; 3 4];
f=10;
u1=parabolic(u0,tlist,'squareb1',p,e,t,c,0,f,1);
pdeplot(p,e,t,'xydata',u1(:,end))

Impossible to run it. I get this error message :

??? Error using ==> times
Matrix dimensions must agree.

Error in ==> pdeasmc at 18
  c3=((cc1.*g1x.*g2x+cc2.*g1y.*g2y).*ar);

Error in ==> assema at 112
    ks1=pdeasmc(it1,it2,it3,np,ar,x,y,sd,u,ux,uy,time,g1x,g1y,g2x,g2y,g3x,g3y,c);

Error in ==> parabolic at 85
  [K,M,F]=assema(p,t,c,a,f,time);

Error in ==> ex_parab at 9
u1=parabolic(u0,tlist,'squareb1',p,e,t,c,0,f,1);

Why is there a matrix dimension problem ? I work on D=2 space, so the gradient is just a column vector, with 2 lines, and 'c' is just a 2by2 matrix in my code.

Does some can help me to understand and fixe it ? Thanks in advance !!

Answer 1

[Bill Greene]

Hi,

PDE Toolbox accepts c-matrices in many different forms depending on whether the matrix is symmetric, unsymmetric or diagonal and also whether the coefficients vary as a function of x. This is discussed more on page 5-21 of the manual.

For your scalar case with a full, unsymmetric matrix, c would be: c=[1 3 2 4]'; Note, this is 4 rows with the coefficients entered by column.

Regards,

Bill

[Jonathan B.]

Hi,

Thank you so much for your help, and for the manual reference !

Best regards,

Jonathan.