scholarly journals Scalable parallelization of the sparse-approximate-inverse (SAI) preconditioner for the solution of large-scale integral-equation problems

2009 ◽  
Author(s):  
T. Malas ◽  
L. Gurel
Keyword(s):  
Integral Equation ◽  
Large Scale ◽  
Approximate Inverse ◽  
Sparse Approximate Inverse

scholarly journals Parallel solution of large-scale free surface viscoelastic flows via sparse approximate inverse preconditioning

2009 ◽  
Vol 157 (1-2) ◽  
pp. 44-54 ◽  
Author(s):  
Zenaida Castillo ◽  
Xueying Xie ◽  
Danny C. Sorensen ◽  
Mark Embree ◽  
Matteo Pasquali
Keyword(s):  
Free Surface ◽  
Large Scale ◽  
Viscoelastic Flows ◽  
Approximate Inverse ◽  
Scale Free ◽  
Parallel Solution ◽  
Sparse Approximate Inverse

scholarly journals Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Han Guo ◽  
Jun Hu ◽  
Hanru Shao ◽  
Zaiping Nie
Keyword(s):  
Integral Equation ◽  
High Efficiency ◽  
Compact Representation ◽  
Mathematical Framework ◽  
Approximate Inverse ◽  
Sparse Approximate Inverse ◽  
Direct Solvers ◽  
Fast Direct Solvers ◽  
The Hierarchical Structure ◽  
Iteration Methods

Hierarchical (H-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics,H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solveH-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure ofH-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solvingH-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

Fast Time Domain Integral Equation Solvers for Large-Scale Electromagnetic Analysis

2004 ◽  
Author(s):  
Eric Michielsssen ◽  
Weng C. Chew ◽  
Jianming Jin ◽  
Balasubramaniam Shanker
Keyword(s):  
Integral Equation ◽  
Time Domain ◽  
Large Scale ◽  
Electromagnetic Analysis ◽  
Fast Time ◽  
Domain Integral ◽  
Time Domain Integral Equation

An adaptive multilevel factorized sparse approximate inverse preconditioning

2017 ◽  
Vol 113 ◽  
pp. 19-24 ◽  
Author(s):  
Jiří Kopal ◽  
Miroslav Rozložník ◽  
Miroslav Tůma
Keyword(s):  
Approximate Inverse ◽  
Sparse Approximate Inverse
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