Hi,
I'm having some trouble constructing a matrix to invert for my time stepping scheme. My scheme is like:
(M_1 + M_2 * (M_1 + dt* M_3)^(-1) * M_4 ) u_{n+1} = M_1 * f( u_{n}, u_{n-1} )
where M_i are my FEM matrices (SparseMatrixDouble), dt is the time step and f is a function of u_{n}, and u_{n-1} which we know. The problem that I am having is building the matrix on the LHS which I will then need to invert.
So far I have the matrices all defined using
m=BilinearForm(V)
m+=SymbolicBFI(u*v)
m.Assemble()
(with variations for their exact forms). And I can build (M_1 + dt* M_3)^(-1) with,
mi = m.mat.CreateMatrix()
mi.AsVector().data = m1.mat.AsVector() + dt*m3.mat.AsVector()
invmi=mi.Inverse(freedofs=V.FreeDofs(),inverse="pardiso")
This is where I am not sure how to proceed in defining (M_1 + M_2 * (M_1 + dt* M_3)^(-1) * M_4 )
Any help on how to do this would be great!
Thanks,
Katie
