Preconditioning the Conjugate Gradient Method for a Hybridized Summation-By-Parts Finite-Difference Discretization of Poisson's Equation with Application to Seismic Simulations

Abstract

We consider the solution by the conjugate gradient (CG) method of the linear systems arising from a hybridized summation-by-parts finite-difference discretization of a Poisson problem that occurs in the simulation of seismic faults. We study the efficacy of three different preconditioning schemes-- Jacobi, incomplete Cholesky, and algebraic multigrid-- at reducing the number of CG iterations required for convergence, finding that while all three preconditioners are effective, the latter two are superior. Code for all of our studies, written in the Julia programming language, is provided.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2022
Accession Number
AD1184946

Entities

People

  • Timothy P. James

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • California
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Fluid Dynamics
  • Fluid Mechanics
  • Geometry
  • Linear Systems
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
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  • Simulations
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  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra