Numerical Solutions to Steady-State Problems with Discontinuities

Abstract

The long term systematic advance of multilevel computational methods has continued in 1989. Highly parallelizable multilevel techniques have been developed for the following mathematical tasks: (1) Solution of general nonlinear PDE systems, including elliptic and nonelliptic, steady-state and time-dependent problems and inverse problems, pointing toward new type of multigrid solvers in fluid dynamics. (2) Fast integral transforms, including FFT on non-uniform grids. (3) Solution of integro-differential equations. (4) Fast multiplication by a dense matrix or its inverse, including O(n) calculation and solution of n body interactions. (5) Global optimization of systems with many local optima, including in particular discrete optimization. (6) Linear programming, at least for spatial problems. (7) Image restoration. (8) Computing behavior of statistical fields; fast calculation of thermodynamic limits. (9) Derivation and super-fast updating of large determinants of grid equations, with special emphasis on Dirac equations. (jhd)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1989
Accession Number
ADA222205

Entities

People

  • David Sidilkover

Organizations

  • Weizmann Institute of Science

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Layer
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Construction
  • Difference Equations
  • Differential Equations
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Fluids
  • High Resolution
  • Integrals
  • Two Dimensional
  • Viscosity

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)