Numerical Algorithms Based on Biorthogonal Wavelets.

Abstract

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1996
Accession Number
ADA307137

Entities

People

  • J. Liandrat
  • Pj Ponenti

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Coefficients
  • Computations
  • Construction
  • Convolution
  • Differential Equations
  • Engineering
  • Equations
  • Fast Fourier Transforms
  • Inverse Problems
  • Mathematics
  • Partial Differential Equations
  • Periodic Functions
  • Polynomials
  • Sequences
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Theoretical Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Space