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.

A Parallel Implementation of a Computational Aeroacoustic Algorithm for Airfoil Noise

1997 ◽  
Vol 05 (04) ◽  
pp. 337-353 ◽  
Author(s):  
David P. Lockard ◽  
Philip J. Morris
Keyword(s):  
Flat Plate ◽  
Message Passing ◽  
Parallel Implementation ◽  
Parallel Computers ◽  
Two Dimensional ◽  
Fortran 90 ◽  
Term Objective

The long-term objective of the research described in this paper is to use CAA methodology and parallel computers to increase the understanding of broadband blade noise. In a systematic progression towards simulations of completely realistic configurations and conditions, some simplified problems that address the important features of the flow are investigated. A two-dimensional, Euler code, implemented using the message passing library and Fortran 90 on the IBM SP2, is used to perform the calculations. Results are presented for the interaction of a vortical gust and a flat plate.

scholarly journals The Local and Parallel Finite Element Scheme for Electric Structure Eigenvalue Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Fubiao Lin ◽  
Junying Cao ◽  
Zhixin Liu
Keyword(s):  
Finite Element ◽  
Eigenvalue Problems ◽  
Three Dimensional ◽  
Local Defect ◽  
Local Refinement ◽  
Element Discretization ◽  
One Dimensional ◽  
Correction Technique ◽  
Polar Coordinate ◽  
Multiscale Finite Element

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.

scholarly journals A Rayleigh quotient method for criticality eigenvalue problems in neutron transport

2020 ◽  
Vol 138 ◽  
pp. 107120
Author(s):  
M.I. Ortega ◽  
R.N. Slaybaugh ◽  
P.N. Brown ◽  
T.S. Bailey ◽  
B. Chang
Keyword(s):  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Rayleigh Quotient
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