35 research outputs found
A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices
This paper describes a multilevel preconditioning technique for solving complex symmetric sparse linear systems. The coefficient matrix is first decoupled by domain decomposition and then an approximate inverse of the original matrix is computed level by level. This approximate inverse is based on low rank approximations of the local Schur complements. For this, a symmetric singular value decomposition of a complex symmetric matix is used. The block-diagonal matrices are decomposed by an incomplete LDLT factorization with the Bunch-Kaufman pivoting method. Using the example of Maxwell's equations the generality of the approach is demonstrated
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A multilevel Schur complement preconditioner with ILU factorization for complex symmetric matrices
This paper describes a multilevel preconditioning technique for solving
complex symmetric sparse linear systems. The coefficient matrix is first
decoupled by domain decomposition and then an approximate inverse of the
original matrix is computed level by level. This approximate inverse is based
on low rank approximations of the local Schur complements. For this, a
symmetric singular value decomposition of a complex symmetric matix is used.
The block-diagonal matrices are decomposed by an incomplete LDLT
factorization with the Bunch-Kaufman pivoting method. Using the example of
Maxwells equations the generality of the approach is demonstrated
On large-scale diagonalization techniques for the Anderson model of localization
We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for large-scale sparse real and symmetric indefinite matrices of the Anderson model
of localization. We compare the Lanczos algorithm in the 1987 implementation by Cullum and Willoughby with the shift-and-invert techniques in the implicitly restarted Lanczos method and in the JacobiāDavidson method. Our preconditioning approaches for the shift-and-invert symmetric indefinite linear system are based on maximum weighted matchings and algebraic multilevel incomplete
LDLT factorizations. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques for the highly ill-conditioned symmetric indefinite Anderson matrices. We demonstrate the effectiveness and the numerical accuracy of these algorithms. Our numerical examples reveal that recent algebraic multilevel preconditioning solvers can accelerate the computation of a large-scale eigenvalue problem corresponding to the Anderson model of localization
by several orders of magnitude