Premium
α‐GMRES: A new parallelizable iterative solver for large sparse non‐symmetric linear systems arising from CFD
Author(s) -
Xu X.,
Qin N.,
Richards B. E.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650150508
Subject(s) - generalized minimal residual method , linear system , solver , preconditioner , parallelizable manifold , discretization , mathematics , linearization , iterative method , diagonally dominant matrix , diagonal , computational fluid dynamics , computer science , biconjugate gradient stabilized method , convergence (economics) , mathematical optimization , algorithm , mathematical analysis , nonlinear system , geometry , physics , quantum mechanics , pure mathematics , invertible matrix , mechanics , economics , economic growth
Linearization of the non‐linear systems arising from fully implicit schemes in computational fluid dynamics often result in a large sparse non‐symmetric linear system. Practical experience shows that these linear systems are ill‐conditioned if a higher than first‐order spatial discretization scheme is used. To solve these linear systems, an efficient multilevel iterative method, the α‐GMRES method, is proposed which incorporates a diagonal preconditioning with a damping factor α so that a balanced fast convergence of the inner GMRES iteration and the outer damping loop can be achieved. With this simple and efficient preconditioning and damping of the matrix, the resulting method can be effectively parallelized. The parallelization maintains the effectiveness of the original scheme due to the algorithm equivalence of the sequential and the parallel versions.