DOI: https://doi.org/10.26089/NumMet.v16r457

Aspects of parallel computing to solve Helmholtz equation by a direct solver with low-rank approximation and the HSS format of data storage

Authors

  • B.M. Glinskiy
  • V.I. Kostin
  • N.V. Kuchin
  • S.A. Solovyev
  • V.A. Cheverda

Keywords:

Helmholtz equation
algorithms for sparse systems of linear algebraic equations
Gaussian elimination method
low-rank approximation
HSS matrix representation
distributed parallel systems
heterogeneous high-performance computing systems

Abstract

An algorithm for solving systems of linear algebraic equations based on the Gaussian elimination method is proposed. The algorithm is aimed to solve boundary value problems for the Helmholtz equation in 3D heterogeneous media. In order to solve linear systems raised from geophysical applications, we developed a parallel version targeted on heterogeneous high-performance computing clusters (MPP and SMP architecture). Using the low-rank approximation technique and the HSS format allows us to solve problems larger than by the use of traditional direct solvers with saving the L-factor in full rank (FR). Using the proposed approach reduces computation time; it is the key-point of 3D geophysical problems. Numerical experiments demonstrate a number of advantages of the proposed low-rank approach in comparison with direct solvers (FR-approaches).

New computational technologies

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Published

2015-10-23

Issue

Vol. 16 (2015): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biographies

B.M. Glinskiy

Siberian Supercomputer Center at the Institute of Computational Mathematics and Mathematical Geophysics of SB RAS
• Executive Director

V.I. Kostin

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Senior Researcher

N.V. Kuchin

Siberian Supercomputer Center at the Institute of Computational Mathematics and Mathematical Geophysics of SB RAS
• Chief Specialist

S.A. Solovyev

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Researcher

V.A. Cheverda

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Head of Laboratory

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