Sparse Approximate Inverse Preconditioner With Parametric Sparsity Pattern Applied to the Macrobasis Function Methods

2018 ◽  
Vol 17 (5) ◽  
pp. 849-852 ◽  
Author(s):  
Carlos Delgado ◽  
Manuel Felipe Catedra
Keyword(s):  
Approximate Inverse ◽  
Sparsity Pattern ◽  
Sparse Approximate Inverse

scholarly journals Application of a Sparsity Pattern and Region Clustering for Near Field Sparse Approximate Inverse Preconditioners in Method of Moments Simulations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Carlos Delgado ◽  
Javier Moreno ◽  
Felipe Cátedra
Keyword(s):  
Method Of Moments ◽  
Near Field ◽  
Least Square ◽  
Approximate Inverse ◽  
Sparsity Pattern ◽  
Field Coupling ◽  
Sparse Approximate Inverse ◽  
Coupling Terms ◽  
Linear Least Square ◽  
Least Square Problems

This document presents a technique for the generation of Sparse Inverse Preconditioners based on the near field coupling matrices of Method of Moments simulations where the geometry has been partitioned in terms of regions. A distance parameter is used to determine the sparsity pattern of the preconditioner. The rows of the preconditioner are computed in groups at a time, according to the number of unknowns contained in each region of the geometry. Two filtering thresholds allow considering only the coupling terms with a significant weight for a faster generation of the preconditioner and storing only the most significant preconditioner coefficients in order to decrease the memory required. The generation of the preconditioner involves the computation of as many independent linear least square problems as the number of regions in which the geometry is partitioned, resulting in very good scalability properties regarding its parallelization.

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

scholarly journals Application of Hierarchical Two-Level Spectral Preconditioning Method for Electromagnetic Scattering from the Rough Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
D. Z. Ding ◽  
G. M. Li ◽  
Y. Y. An ◽  
R. S. Chen
Keyword(s):  
Rough Surface ◽  
Electromagnetic Scattering ◽  
Fast Multipole Method ◽  
Scattering Problems ◽  
Approximate Inverse ◽  
Sparse Approximate Inverse ◽  
Preconditioning Method ◽  
Speed Up ◽  
Spectral Preconditioner ◽  
Field Integral

The higher-order hierarchical Legendre basis functions combining the electrical field integral equations (EFIE) are developed to solve the scattering problems from the rough surface. The hierarchical two-level spectral preconditioning method is developed for the generalized minimal residual iterative method (GMRES). The hierarchical two-level spectral preconditioner is constructed by combining the spectral preconditioner and sparse approximate inverse (SAI) preconditioner to speed up the convergence rate of iterative methods. The multilevel fast multipole method (MLFMM) is employed to reduce memory requirement and computational complexity of the method of moments (MoM) solution. The accuracy and efficiency are confirmed with a couple of numerical examples.

A Dynamic Pattern Factored Sparse Approximate Inverse Preconditioner on Graphics Processing Units

2019 ◽  
Vol 41 (3) ◽  
pp. C139-C160 ◽  
Author(s):  
Massimo Bernaschi ◽  
Mauro Carrozzo ◽  
Andrea Franceschini ◽  
Carlo Janna
Keyword(s):  
Graphics Processing Units ◽  
Approximate Inverse ◽  
Dynamic Pattern ◽  
Sparse Approximate Inverse ◽  
Graphics Processing

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
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