Yogi A. Erlangga
Delft Univ. of
Technology, Dept. Appl. Math. Anal.,
Mekelweg 8, 2628
CD Delft, The Netherlands
Correspondence:
y.a.erlangga@ewi.tudelft.nl
In this paper an iterative method to solve the Helmholtz equation
In its general formulation, the preconditioning operator is defined as
To investigate the convergence of multigrid as a solver for (2)
and as a preconditioner for (1),
analyses based on Rigorous Fourier Analysis (RFA) is done. It is found
from this analysis that standard multigrid components can still be applied to
(2),
with a slight modification to the matrix-dependent interpolation operator by de
Zeeuw. This interpolation is effective for cases where heterogeneity is present.
Furthermore, from RFA we also find that the combination
results in a robust preconditioner for (1).
For this combination, V(1,1) cycle with Jacobi smoother with small
underrelaxation factor (
)can be applied.
Table 1
shows Bi-CGSTAB iterations preconditioned by (2)
for Helmholtz problems with constant . CPU time is
measured on a Pentium IV Linux PC. These results, especially with
, show the robustness of
the method.
Problems with heterogeneity, which are of our main interest, will be presented during the talk.