Generalized Non-Linear Minimal Residual (GNLMR) Method for Optimal Multistep Iterative Algorithms

Abstract

A new Distributed Minimal Residual (DMR) method for the acceleration of explicit iterative algorithms for the numerical solution of systems of partial differential equations has been developed. The method is based on the idea of allowing each partial differential equation in the system to approach the converged solution at its own optimal speed while at the same time communicating with the rest of the equations in the system. The DMR method belongs to a general class of the extrapolation techniques in which the solution is updated using information from a number of consecutive time steps in such a way that the L2 norm of future residual is minimized. Unlike in other similar methods, each component of the solution vector is updated using a separate sequence of acceleration factors. The idea of using different acceleration factors for each component of a solution vector is similar to that of dynamic preconditioning. This allows each equation to evolve at its own optimal convergence rate.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 06, 1988
Accession Number
ADA204322

Entities

People

  • George S. Dulikravich

Organizations

  • Pennsylvania State University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Sensors
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundary Layer
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Hydrodynamics
  • Incompressible Flow
  • Mathematics
  • Mechanical Engineering
  • Navier Stokes Equations
  • Numerical Analysis
  • Partial Differential Equations
  • Physics Laboratories
  • Two Dimensional

Readers

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