Solving PDEs: Number of rows required in output of user defined coefficient functions

Hello, I am trying to solve an inhomogenous wave equation using a script (not PDETool) and the hyperbolic PDE solver. My coefficients are quite complicated so I am writing my own functions to describe them. I understand that the coefficient array the function outputs must have as many columns as mesh elements, but what about the number of rows? I currently only have one row but I get errors from 'pdeasma' indicating that matrix dimensions must agree. When I give the coefficient a single scalar value it's fine, so I am confident the error has to do with my coefficient function. My coefficients are only dependent on position in the mesh (not time or initial conditions). Thanks a lot!

Answer 1

[Bill Greene]

Hi Susannah,

I think I can give you some help on this. I'll discuss the c-coefficient since that is the most complex one.

You didn't say whether you have more than one PDE in your system. If you have only one (i.e. a scalar PDE), the number of rows for the c-coefficient can be 1, 2, 3, or 4. For this case, you can think of c as a 2x2 matrix. If your properties are the same in the x and y directions, you need to input only one row (c11=c22=c). Otherwise, you enter the terms from the 2x2 matrix row by row. For example, if you want to enter the full 2 x 2 matrix, you would need 4 rows.

For the system case (N>1), there is a bewildering number of options depending on which terms in the 2N x 2N c-matrix you need to describe your equations. Those options are described here:

http://www.mathworks.com/help/pde/ug/c.html

One final tip: you can always define your c-coefficient with 2*N*2*N rows but, usually, many of those entries will be zero.

Hope that helps.

Bill

[Susannah]

Thanks Bill. It's a scalar PDE. I'm still confused about entering coefficients. My c and a coefficients are -1 and 0, respectively, so I am just entering those as scalar numbers. For d and f, I have a one row array with each column containing the appropriate coefficient for the corresponding mesh point. Should I have more rows for these coefficients?

[Bill Greene]

For a scalar PDE, d, f, and a must be scalars (one row).

Bill

PS: FYI, you could also have defined c as:

c = [-1 -1]';
c = [-1 0 -1]';
c = [-1 0 0 -1]';

They are all equivalent to the most convenient form

c = -1;

which you chose.