Scale the inverse of matrix

NGSolve
1

Dear all,

I have tried implementing the MHSS preconditioner for the CG solver in NGSolve.

P = (1 + j)(B + C) where B is the real part and C is the imaginary part.
I could calculate
a_pre_inv = a_pre.Inverse(fes_pre.FreeDofs(), inverse="sparsecholesky") where a_pre is B + C.
Is there any way to scale this inverse with 1/(1-1j) and use this matrix as a preconditioner for the CG solver of the complex system?

Any help is highly appreciated.

Best regards,
VC

2

Maybe there is even an easier way, but one way is to derive from BaseMatrix and implement the scaling there. Something like this:

class ScaledBaseMat(BaseMatrix):
  def __init__(self, mat):
    self.mat = mat
    super().__init__()

  def Mult(self, x, y):
    y.data = self.mat * x
    y[:] *= 1/(1-1j)

and then use this matrix in your preconditioner.

See here for an example of such a BaseMatrix overload:
https://docu.ngsolve.org/latest/i-tutorials/unit-2.1.2-blockjacobi/blockjacobi.html#Implement-a-forward-backward-GS-preconditioner

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