The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Algebraic Two-Level Preconditioners for the Schur Complement Method
SIAM Journal on Scientific Computing
Domain Decomposition Algorithms for the Partial Differential Equations of Linear Elasticity
Domain Decomposition Algorithms for the Partial Differential Equations of Linear Elasticity
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We present a new parallelizable preconditioner that is used as the local component of a two-level preconditioner similar to BPS. On 2D model problems that exhibit either high anisotropy or discontinuity, we demonstrate its attractive numerical behaviour and compare it with the regular BPS. To alleviate the construction cost of this new preconditioner, that requires the computation of the local Schur complements, we propose a cheap alternative based on Incomplete Cholesky factorization, that reduces the computational cost but retains the good numerical features of the preconditioner.