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

Authors:
Haim Waisman;Jacob Fish;Raymond S. Tuminaro;John N. Shadid
Affiliations:
Department of Civil, Mechanical and Aerospace Engineering, Rensselaer Polytechnic Institute, 44 Brinsmade Terrace, Troy, NY 12180-3590, United States;Department of Civil, Mechanical and Aerospace Engineering, Rensselaer Polytechnic Institute, 44 Brinsmade Terrace, Troy, NY 12180-3590, United States;Sandia National Laboratories, P.O. Box 969, MS 9159, Livermore, CA 94551, United States;Sandia National Laboratories, P.O. Box 5800, MS 0316, Albuquerque, NM 87185, United States
Venue:
Journal of Computational Physics
Year:
2005

Citing 5
Cited 0

LAPACK's user's guide

LAPACK's user's guide
Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations

Journal of Computational Physics
A Class of Spectral Two-Level Preconditioners

SIAM Journal on Scientific Computing
Performance of fully coupled domain decomposition preconditioners for finite element transport/reaction simulations

Journal of Computational Physics

Quantified Score

Hi-index	31.45

Visualization

Abstract

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 GGB@a 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.