Efficient Approximate Inverse Preconditioning Techniques for Reduced Systems on Parallel Computers

2010 ◽  
pp. 203-228
Author(s):  
K. Moriya ◽  
L. Zhang ◽  
T. Nodera
Keyword(s):  
Parallel Computers ◽  
Approximate Inverse ◽  
Preconditioning Techniques

Preconditioned Symmetric Linear BCG Method for Solving FEM Electromagnetism Problems

2012 ◽  
Vol 214 ◽  
pp. 610-614 ◽  
Author(s):  
Yue Hui Li
Keyword(s):  
Three Dimensional ◽  
Fem Analysis ◽  
Approximate Inverse ◽  
Preconditioning Techniques ◽  
Electromagnetic Problems ◽  
Sparse Approximate Inverse ◽  
Edge Based ◽  
Large Linear Systems ◽  
Simulation Time ◽  
Operator Scheme

A new preconditioning technique for solving large linear systems arising from edge-based finite element method (FEM) analysis of three-dimensional (3-D) electromagnetic problems is presented. This method is achieved by applying a shifted-Laplace operator scheme and sparse approximate inverse to symmetric linear BCG (LBCG). The main purpose is to generate a more robust and efficient preconditioner. Numerical results on several electromagnetic problems show that, by comparing with other conventional preconditioning techniques, this technique is more efficient and robust, and can greatly reduce the simulation time.

scholarly journals Parallel Rayleigh Quotient Optimization with FSAI-Based Preconditioning

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Luca Bergamaschi ◽  
Angeles Martínez ◽  
Giorgio Pini
Keyword(s):  
Eigenvalue Problems ◽  
Parallel Implementation ◽  
Rayleigh Quotient ◽  
Parallel Computers ◽  
Symmetric Matrices ◽  
Approximate Inverse ◽  
Element Discretization ◽  
Sparse Approximate Inverse ◽  
Large Size ◽  
Fortran 90

The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse-approximate-inverse- (FSAI-) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI-IC preconditioner, which combines the FSAI and the Block Jacobi-IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallelhyprepackage, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI-Fortran 90 language and exhibits good scalability up to one thousand processors.

Microstructures in Elastic Media

1994 ◽  
Author(s):  
Nhan Phan-Thien ◽  
Sangtae Kim
Keyword(s):  
Computational Methods ◽  
High Performance ◽  
Chemical Engineering ◽  
Elliptic Partial Differential Equations ◽  
Parallel Computers ◽  
Computational Algorithms ◽  
Applied Physics ◽  
Advanced Students ◽  
Particulate Solids ◽  
Modeling Software

This monograph describes various methods for solving deformation problems of particulate solids, taking the reader from analytical to computational methods. The book is the first to present the topic of linear elasticity in mathematical terms that will be familiar to anyone with a grounding in fluid mechanics. It incorporates the latest advances in computational algorithms for elliptic partial differential equations, and provides the groundwork for simulations on high performance parallel computers. Numerous exercises complement the theoretical discussions, and a related set of self-documented programs is available to readers with Internet access. The work will be of interest to advanced students and practicing researchers in mechanical engineering, chemical engineering, applied physics, computational methods, and developers of numerical modeling software.

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