[petsc-users] solve complex linear system: real or complex formulation

[Xiangdong Liang]

Hello everyone,

I am solving a complex linear system C x = d, where C= A+ iB (A, B are
real), in sparse-direct solver. So far, I use the real formulation by
solving the linear system [A, -B; B,A].  The reason we chose this
approach is to use the property of that the imaginary part B in our
problem is sparser than A. However, I just found that the spare-direct
solver cannot benefit from this property.

Now, I am thinking to re-implement it in to complex version by solving
Cx=d in the complex version. Of course, complex formulation would
perform better for iterative solvers since it only has half
eigenvalues than the corresponding real formulations. I am wondering
the comparison between real and complex formulation for sparse-direct
solver. Can anyone share experiences on this? Thanks.

Xiangdong