STABILIZING AND ACCELERATING SOLUTION OF HARMONIC BALANCE EQUATION SYSTEM USING THE LU-SGS AND BLOCK JACOBI METHODS

摘要

The paper presents the combination of the Lower Upper Symmetric Gauss Seidel (LU-SGS) method and the block Ja-cobi method for stabilizing and accelerating the solution of a harmonic balance equation system. First the baseline LU-SGS procedure for a harmonic balance equation system with explicit discretization of the time spectral source term is derived. The LU-SGS method, different from its original application as an implicit time marching scheme, is used as an implicit residual smoother, allowing big CFL numbers (in order of 1000s), within the Runge-Kutta explicit time marching loops. Then the block Jacobi method is introduced to augment solution stability for the solution of a harmonic balance equation system under situation where grid reduced frequency is in the order of 10. Results are presented to show the effectiveness of the combination of LU-SGS and the block Jacobi method on the solution stabilization and acceleration. The influence of the number of Jacobi iterations on solution convergence is also investigated.