nonzero m and d coefficients for Matlab PDE

Hello, everyone!

I am trying to solve the 2D problem with Matlab PDE and need to specify both mass (m) and damping (d) to be nonzero.

Workflow in short:

create model with

model = createpde(N);

specify geometry ...

coefficients:

specifyCoefficients(model, 'm', rho, 'd', d, 'c', c, 'a', 0, 'f', f);

and solve it:

result = solvepde(model,time);

I got stuck having the error:

Error using pde.CoefficientAssignment/checkMandD (line 303)

When both 'm' and 'd' coefficients are nonzeros, the 'd' coefficient must be a matrix.

In the documentation to the function "specifyCoefficients" it is said:

Note: If the PDE to solve has both 'm' and 'd' coefficients that are

non-zero, then 'd' must be a matrix that has the same size as

the discretized mass matrix (not to be confused with 'm').

What is the correct way to specify 'd' coefficient when mass is nonzero?

Answer 1

[Ravi Kumar]

Refer to this documentation:

https://www.mathworks.com/help/pde/ug/pde.pdemodel.specifycoefficients.html#bu7pwf5

d has to be a sparse matrix when m is non-zero.

[Siarhei Hladyshau]

Thank you!

[Joanna Chang]

I am following the instructions here but it is unclear how to create this sparse matrix. I have a PDE system with 2 equations and two variables u1 and u2, and d should be 0 in the first equation and 1 for u2 in the second equation, such that d=[0 0; 0 1], what should the matrix be if result.M is of size 120x120?