Semi-orthogonal wavelets for elliptic variational problems

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In this paper the authors give a construction of wavelets which are (a) semi-orthogonal with respect to an arbitrary elliptic bilinear form a({center_dot},{center_dot}) on the Sobolev space H{sub 0}{sup 1}((0, L)) and (b) continuous and piecewise linear on an arbitrary partition of [0, L]. They illustrate this construction using a model problem. They also construct alpha-orthogonal Battle-Lemarie type wavelets which fully diagonalize the Galerkin discretized matrix for the model problem with domain IR. Finally they describe a hybrid basis consisting of a combination of elements from the semi-orthogonal wavelet basis and the hierarchical Schauder basis. Numerical experiments indicate that this ... continued below

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15 p.

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Hardin, D.P. & Roach, D.W. April 1, 1998.

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  • Hardin, D.P. Vanderbilt Univ., Nashville, TN (United States). Mathematics Dept.
  • Roach, D.W. Sandia National Labs., Albuquerque, NM (United States)

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

In this paper the authors give a construction of wavelets which are (a) semi-orthogonal with respect to an arbitrary elliptic bilinear form a({center_dot},{center_dot}) on the Sobolev space H{sub 0}{sup 1}((0, L)) and (b) continuous and piecewise linear on an arbitrary partition of [0, L]. They illustrate this construction using a model problem. They also construct alpha-orthogonal Battle-Lemarie type wavelets which fully diagonalize the Galerkin discretized matrix for the model problem with domain IR. Finally they describe a hybrid basis consisting of a combination of elements from the semi-orthogonal wavelet basis and the hierarchical Schauder basis. Numerical experiments indicate that this basis leads to robust scalable Galerkin discretizations of the model problem which remain well-conditioned independent of {epsilon}, L, and the refinement level K.

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15 p.

Notes

OSTI as DE98004760

Source

  • International wavelet conference Tangier 98, Tangier (Morocco), 13 Apr 1998

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  • Other: DE98004760
  • Report No.: SAND--98-0975C
  • Report No.: CONF-980434--
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 672012
  • Archival Resource Key: ark:/67531/metadc704415

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  • April 1, 1998

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • Aug. 23, 2016, 3:21 p.m.

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Hardin, D.P. & Roach, D.W. Semi-orthogonal wavelets for elliptic variational problems, article, April 1, 1998; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc704415/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.