Incomplete Line LU for Discretized Coupled PDE's as Preconditioner in Bi-CGSTAB

摘要

A variant of the recently developed Bi-CGSTAB method is applied to solving thelinear systems that typically occur when applying Newton's method to a discretized set of coupled elliptic Partial Differential Equations (PDE) in two dimensions. Bi-CGSTAB is a reformulation of the Induced Dimension Reduction (IDR) method and cures the irregular convergence behavior of the Conjugate Gradient-Squared (CG-S) method. The Incomplete Line LU relaxation is generalized for the case of coupled equations and applied as preconditioner. Both an eligible stopping and restart criterion are developed for the Bi-CGSTAB method. Numerical experiments are performed for problems stemming from the area of semiconductor modeling and an aquifer problem. For the latter problem a comparison is made with an existing multigrid algorithm in which Incomplete Line LU relaxation is used as a smoothing procedure.