Parallel implementation of a sparse approximate inverse preconditioner

1996 ◽  
pp. 63-74 ◽  
Author(s):  
Vaibhav Deshpande ◽  
Marcus J. Grote ◽  
Peter Messmer ◽  
William Sawyer
Keyword(s):  
Parallel Implementation ◽  
Approximate Inverse ◽  
Sparse Approximate Inverse

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.

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
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