Preconditioning by Fast Direct Methods for Non-Self-Adjoint Nonseparable Elliptic Equations.

Abstract

We consider the use of fast direct methods as preconditioners for iterative methods for computing the numerical solution of non-self-adjoint elliptic boundary value problems. We derive bounds on convergence rates that are independent of discretization mesh size. For two-dimensional problems on rectangular domains, discretized on an nxn grid, these bounds lead to asymptotic operation counts of O(n squared log n 1/log epsilon) to achieve relative error epsilon and O(n squared (log n) squared) to reach truncation error.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1983
Accession Number
ADA139360

Entities

People

  • H. C. Elman
  • Martin H. Schultz

Organizations

  • Yale University

Tags

DTIC Thesaurus Topics

  • Boundary Layer
  • Boundary Value Problems
  • Computations
  • Computer Science
  • Computers
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Iterations
  • Linear Algebra
  • Linear Systems
  • New York
  • Numerical Analysis
  • Partial Differential Equations
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.