SVD Stabilized Block Preconditioning for Large Dense Linear Systems from Electromagnetic Applications

Yin Wang

Email: ywangf@csr.uky.edu
Postal address: Department of Computer Science, University of Kentucky, Lexington, KY, 40506-0046, USA

In computational electromagnetics, we consider preconditioning techniques combined with the Krylov iterative methods to solve large dense linear systems, where the coefficient matrix are complex-valued matrix arising from discretizd hybrid integral equations. Due to its easy implementation, the block diagonal preconditioner has been used to accelerate the convergence rate of Krylov iterative methods. Previous studies indicate that, in some cases, the block diagonal preconditioner makes the convergence more slowly or even diverges. In this paper, we propose a new block preconditioner based on the singular value decomposition (SVD) to stabilize the inverse of the diagonal blocks. We construct the SVD stabilized block preconditioner by applying SVD to each individual block generated from the multilevel fast multipole algorithm (MLFMA). Our experimental results show that the SVD stabilized block preconditioner reduces the number of iterations compared with the block diagonal preconditioner and reduce the overall CPU time.