Acceleration of the generalized global basis (GGB) method for nonlinear problems

Two heuristic strategies intended to enhance the performance of the generalized global basis (GGB) method [H. Waisman, J. Fish, R.S. Tuminaro, J. Shadid, The Generalized Global Basis (GGB) method, International Journal for Numerical Methods in Engineering 61(8), 1243–1269] applied to nonlinear systems are presented. The standard GGB accelerates a multigrid scheme by an additional coarse grid correction that filters out slowly converging modes. This correction requires a potentially costly eigen calculation. This paper considers reusing previously computed eigenspace information. The GGBα scheme enriches the prolongation operator with new eigenvectors while the modified method (MGGB) selectively reuses the same prolongation. Both methods use the criteria of principal angles between subspaces spanned between the previous and current prolongation operators. Numerical examples clearly indicate significant time savings in particular for the MGGB scheme.

提出了两种旨在提高广义全局基（GGB）方法性能的启发式策略，该方法应用于非线性系统，见[H. 魏斯曼，J. 菲什，R.S. 图米纳罗，J. 沙迪德，《广义全局基（GGB）方法》，《国际工程数值方法杂志》61(8)，1243 - 1269]。标准的GGB方法通过一个额外的粗网格校正来加速多重网格方案，该校正过滤掉收敛缓慢的模式。这种校正需要进行可能成本较高的特征值计算。本文考虑重新使用先前计算的特征空间信息。GGBα方案用新的特征向量丰富了延拓算子，而改进的方法（MGGB）有选择地重新使用相同的延拓。这两种方法都使用了先前和当前延拓算子所张成的子空间之间的主角度标准。数值例子清楚地表明，特别是对于MGGB方案，节省了大量时间。