elliptic PDE with variable coefficient

Hello,

I am desperately trying to solve the following equation (in 2D) :

-(laplacian)u + u =1

This is basically an elliptic PDE with

c=1 , f=1 and a= B(x,y).

B(x,y) is a function I have created that doesn't have any closed form. Here's the code for B(x,y):

I entered c=1 , f=1 and a= B(x,y) in the pde specification but I cannot solve the equation as I get the following error

Expression evaluates to wrong size. Must be scalar or row vector. In a system case, pass first or second row; for example u(2,:)

Can somebody help me fix this ?

Thank you

[Geoff Hayes]

Ann - please describe what you mean by I entered c=1 , f=1 and a= V(x,y). in the pde specification but I cannot solve the equation as I get the following error. What line of code are you calling that generates the error? What is the pde specification?

[ann]

I was talking about the PDE toolbox in Matlab. In the PDE toolbox, you can choose the type of the equation you are trying to solve (in the menu -> PDE -> PDE specifications ..). Here my equation is an elliptic one : ie. it takes the form

-div(c*grad(u))+a*u=f

so I chose

c=1 , a= V(x,y) , f=1

Answer 1

[Bill Greene]

The input arguments, x and y are equal length row vectors of x and y coordinates where the a coefficient must be defined. If this length (number of columns) is n, the output argument, v, must be a matrix with dimensions 1 x n (i.e. a row vector). The line

v = M(intx,inty);

is returning an n x n matrix; that is the reason for the error message.

[ann]

Thank you for your answer !

The x and y in V(x,y) are the spatial coordinates of the point where we want to calculate V, that's why v is a n x n matrix. v[i][j]= Potentiel at the point (x[i],y[j]).

Can you explain what does x , y represent in Matlab and what should the function return ?

[Bill Greene]

Yes, x and y are spatial locations in the mesh where the a-coefficient must be defined. The returned value must be a row vector with values at just those points. You are returning a matrix with n x n points where what is required is a row vector with values at the n locations. The simplest way to understand and implement this (though not particularly efficient) is with this snippet of code:

v = zeros(1, length(x))
for i=1:length(x)
  v(i) = M(intx(i), inty(i));
end

[ann]

Thank you