Homogenization via Sequential Projection to Nested Subspaces Spanned by Orthogonal Scaling and Wavelet Orthonormal Families of Functions

Abstract

This report presents a summary introduction to the homogenization procedure in numerical methods via sequential projections onto nested subspaces spanned by mutually orthogonal scaling and wavelet orthonormal families of functions. The ideas behind the technique of multi-resolution analysis unfold from the theory of linear operators in Hilbert spaces. The homogenization procedure through successive multiresolution projections is presented, followed by a numerical example of sequential analysis and synthesis of a simple signal illustrating the application of the theory. A structural example shows a practical application of multi-resolution analysis to the displacement response of a cantilever with highly heterogeneous elasticity subjected to a concentrated load at the tip. An introductory appendix describes the reproducing kernel methods of mathematical representation of a given field.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2008
Accession Number
ADA485319

Entities

People

  • Luis A. De Béjar

Organizations

  • Engineer Research and Development Center

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Displacement
  • Elastic Properties
  • Engineers
  • Equations
  • Filters
  • Frequency
  • Frequency Domain
  • Frequency Response
  • High Pass Filters
  • Hilbert Space
  • Low Pass Filters
  • Mathematics
  • Mechanics
  • Modulus Of Elasticity
  • Sequences
  • Sequential Analysis
  • Signal Processing

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Graph Algorithms and Convex Optimization.
  • Image Processing and Computer Vision.

Technology Areas

  • Space