Journal ArticleDOI
MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies
TLDR
A class of parallel multistep successive preconditionsing strategies to enhance efficiency and robustness of standard sparse approximate inverse preconditioning techniques are developed.Abstract:
We develop a class of parallel multistep successive preconditioning strategies to enhance efficiency and robustness of standard sparse approximate inverse preconditioning techniques. The key idea is to compute a series of simple sparse matrices to approximate the inverse of the original matrix. Studies are conducted to show the advantages of such an approach in terms of both improving preconditioning accuracy and reducing computational cost, compared to the standard sparse approximate inverse preconditioners. Numerical experiments using one prototype implementation to solve a few sparse matrices on a distributed memory parallel computer are reported.read more
Citations
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Journal ArticleDOI
FSAIPACK: A Software Package for High-Performance Factored Sparse Approximate Inverse Preconditioning
TL;DR: A fresh software package, called FSAIPACK, is developed for shared memory parallel machines that collects all available algorithms for computing FSAI preconditioners and allows for combining different techniques according to any specified strategy, hence enabling the user to thoroughly exploit the potential of each preconditionser, in solving any peculiar problem.
Journal ArticleDOI
Application of an improved P(m)-SOR iteration method for flow in partially saturated soils
TL;DR: In this paper, the potential of using the successive over-relaxation iteration method with polynomial preconditioner (P(m)-SOR) to solve variably saturated flow problems described by the linearized Richards' equation was studied.
Sparse Approximate Inverses for Preconditioning, Smoothing, and Regularization
TL;DR: The thesis presents new variants as well as parallel implementations of (M)SPAI and FSPAI as smoother for multigrid and as regularizing preconditioner for iterative regularization methods to reconstruct blurred and noisy signals such as images.
Journal ArticleDOI
Parallel simulation of anisotropic diffusion with human brain DT-MRI Data
TL;DR: The experimental results of the diffusion simulations on a parallel supercomputer show that the sparse approximate inverse preconditioning strategy, which is robust and efficient with good scalability, gives a much better overall performance than the banded-block-diagonal preconditionser.
Journal ArticleDOI
Orthogonal Projections of the Identity: Spectral Analysis and Applications to Approximate Inverse Preconditioning
TL;DR: The effectiveness of the optimal approximate inverse preconditionsers (parametrized by any vectorial structure) improves at the same time as the smallest singular value (or the smallest eigenvalue's modulus) of the corresponding preconditioned matrices increases to $1.
References
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Book
Iterative Methods for Sparse Linear Systems
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Book
Iterative Solution of Large Linear Systems
TL;DR: The ASM preconditioner B is characterized by three parameters: C0, ρ(E) , and ω , which enter via assumptions on the subspaces Vi and the bilinear forms ai(·, ·) (the approximate local problems).
Book
Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations
TL;DR: 1. One level algorithms 2. Two level algorithms 3. Multilevel algorithms 4. Substructuring methods 5. A convergence theory
Book
Introduction to Parallel Computing
TL;DR: Message Passing Interface, POSIX threads and OpenMP have been selected as programming models and the evolving application mix of parallel computing is reflected in various examples throughout the book.
Journal ArticleDOI
Parallel Preconditioning with Sparse Approximate Inverses
Marcus J. Grote,Thomas Huckle +1 more
TL;DR: A parallel preconditioner is presented for the solution of general sparse linear systems of equations using a sparse approximate inverse computed explicitly and then applied as a preconditionser to an iterative method.