Animproved Block Diagonal Preconditioners for Non-symmetric Indefinite Linear Systems

Block preconditioners for symmetric indefinite linear systems

This paper presents a systematic theoretical and numerical evaluation of three common block preconditioners in a Krylov subspace method for solving symmetric indefinite linear systems. The focus is on large-scale real world problems where block approximations are a practical necessity. The main illustration is the performance of the block diagonal, constrained, and lower triangular precondition...

Block-Diagonal and Constraint Preconditioners for Nonsymmetric Indefinite Linear Systems. Part I: Theory

We study block-diagonal preconditioners and an efficient variant of constraint preconditioners for general two-by-two block linear systems with zero (2,2)-block. We derive block-diagonal preconditioners from a splitting of the (1,1)-block of the matrix. From the resulting preconditioned system we derive a smaller, so-called related system that yields the solution of the original problem. Solvin...

Block Diagonal Preconditioners for the Schur Complement Method Block Diagonal Preconditioners for the Schur Complement Method

We present numerical methods for solving systems of linear equations originated from the discretisation of two-dimensional elliptic partial diierential equations. We are interested in diierential equations that describe heterogeneous and anisotropic phenomena. We use a nonoverlapping domain decomposition method for solving the linear systems. We describe new local preconditioners for the interf...

Preconditioners for Indefinite Linear Systems Arising in Surface Parameterization

Low Rank Off-diagonal Block Preconditioners for Solving Sparse Linear Systems on Parallel Computers

For a sparse linear system Ax = b, preconditioners of the form C = D + L+ U , where D is the block diagonal part of A (or incomplete factorization approximation of its blocks), and L and U are block strictly lower and upper triangular matrices composed of low-ranks approximations of the respective blocks of A, are examined. C is applied directly, by solving Cz = w, or partially, by applying one...