scholarly journals Fast direct solvers for Poisson equation on 2D polar and spherical geometries

2001 ◽  
Vol 18 (1) ◽  
pp. 56-68 ◽  
Author(s):  
Ming-Chih Lai ◽  
Wei-Cheng Wang
Keyword(s):  
Poisson Equation ◽  
Direct Solvers ◽  
Fast Direct Solvers

scholarly journals On a Construction of Fast Direct Solvers

2003 ◽  
Vol 48 (3) ◽  
pp. 225-236
Author(s):  
Milan Práger
Keyword(s):  
Direct Solvers ◽  
Fast Direct Solvers

Fast Direct Solvers for Piecewise Hermite Bicubic Orthogonal Spline Collocation Equations

1992 ◽  
Vol 29 (1) ◽  
pp. 156-173 ◽  
Author(s):  
Bernard Bialecki ◽  
Graeme Fairweather ◽  
Karin R. Bennett
Keyword(s):  
Spline Collocation ◽  
Direct Solvers ◽  
Orthogonal Spline Collocation ◽  
Fast Direct Solvers

scholarly journals The value of continuity: Refined isogeometric analysis and fast direct solvers

2017 ◽  
Vol 316 ◽  
pp. 586-605 ◽  
Author(s):  
Daniel Garcia ◽  
David Pardo ◽  
Lisandro Dalcin ◽  
Maciej Paszyński ◽  
Nathan Collier ◽  
...  
Keyword(s):  
Isogeometric Analysis ◽  
Direct Solvers ◽  
Fast Direct Solvers

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.

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