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Global‐basis two‐level method for indefinite systems. Part 2: computational issues
Author(s) -
Qu Yong,
Fish Jacob
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20000930)49:3<461::aid-nme982>3.0.co;2-s
Subject(s) - basis (linear algebra) , smoothing , mathematics , convergence (economics) , mathematical optimization , context (archaeology) , computer science , lanczos resampling , helmholtz free energy , basis function , helmholtz equation , algorithm , mathematical analysis , geometry , paleontology , eigenvalues and eigenvectors , physics , quantum mechanics , economics , computer vision , biology , boundary value problem , economic growth
Algorithmic aspects and computational efficiency of the global‐basis two‐level method are investigated in the context of symmetric indefinite system of equations. The algorithm includes efficient construction of the global‐basis prolongator using Lanczos vectors, predictor–corrector smoothing procedures, and a heuristic two‐level feedback loop aimed at ensuring convergence. Numerical experiments consisting of 3D Helmholtz equations and shear banding problems with strain softening demonstrate the excellent performance of the method. Copyright © 2000 John Wiley & Sons, Ltd.