Grid Adaptation and Parabolic Equations by Multigrid Techniques.

Abstract

The long-term goal of our research at the Weizmann Institute is the development of multi-level methods for solving all types of large-scale problems in science and engineering. In addition to an extensive and diverse development of multigrid solvers for differential and integral equations, completely new multilevel approaches have recently been introduced to the areas of large-scale global optimization statistical physics and calculation of many-body interactions (see our review). The purpose of our study was to provide criteria for optimizing meshsizes near singularities and to develop fast and flexible multigrid methods for creating the nonuniform grids, their difference equations and their solutions. For simplicity, the Poisson problem was studied, with singularities introduced either in the forcing terms (algebraic singularities or sources) or in the shape of the boundaries (reentrant corners). Local refinements were created by multigrid structures in which some extra finer levels cover increasingly narrower neighborhoods of the singularity, as proposed in another work.

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Document Details

Document Type
Technical Report
Publication Date
Oct 31, 1987
Accession Number
ADA191539

Entities

People

  • Achi Brandt

Organizations

  • Weizmann Institute of Science

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Availability
  • Classification
  • Computational Fluid Dynamics
  • Computational Science
  • Computers
  • Contracts
  • Difference Equations
  • Differential Equations
  • Equations
  • Extrapolation
  • Formulas (Mathematics)
  • Integral Equations
  • Security
  • Steady State
  • Truncation

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Technical Research and Report Writing.