Tensor coefficient Poisson equation

[kaigaox]

Hi, does anyone konw how to use MFEM to solve a tensor coefficient Poisson equation in the form of

where c is a 3x3 tensor in the form of

I want to solve the Poisson in such a way that, I have a cube domain that has n1xn2xn3 elements, and for each element, I want to specify some value for the c tensor.

Thanks a lot

[jandrej]

Hello,

does one of the MatrixCoefficients work for you?

[v-dobrev]

You can define a custom MatrixCoefficicient, e.g. ElementwiseMatrixCoefficient, to use with the DiffusionIntegrator in a way very similar to Example 1.

For the ElementwiseMatrixCoefficient you just need to implement the virtual method Eval(DenseMatrix &K, ElementTransformation &T, const IntegrationPoint &ip) -- you need to set the output parameter K based on the input element index which is given by T.ElementNo.