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Title: Semi-orthogonal wavelets for elliptic variational problems

Abstract

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.

Authors:
 [1];  [2]
  1. Vanderbilt Univ., Nashville, TN (United States). Mathematics Dept.
  2. Sandia National Labs., Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Labs., Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Financial Management and Controller, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
OSTI Identifier:
672012
Report Number(s):
SAND-98-0975C; CONF-980434-
ON: DE98004760; BR: YB0100000; TRN: AHC2DT07%%171
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Conference
Resource Relation:
Conference: International wavelet conference Tangier 98, Tangier (Morocco), 13 Apr 1998; Other Information: PBD: Apr 1998
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; DIFFERENTIAL EQUATIONS; VARIATIONAL METHODS; GALERKIN-PETROV METHOD; MATRICES; MATHEMATICAL SPACE; TRANSFORMATIONS; ALGORITHMS

Citation Formats

Hardin, D.P., and Roach, D.W. Semi-orthogonal wavelets for elliptic variational problems. United States: N. p., 1998. Web.
Hardin, D.P., & Roach, D.W. Semi-orthogonal wavelets for elliptic variational problems. United States.
Hardin, D.P., and Roach, D.W. Wed . "Semi-orthogonal wavelets for elliptic variational problems". United States. https://www.osti.gov/servlets/purl/672012.
@article{osti_672012,
title = {Semi-orthogonal wavelets for elliptic variational problems},
author = {Hardin, D.P. and Roach, D.W.},
abstractNote = {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.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1998},
month = {4}
}

Conference:
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