Semi-orthogonal wavelets for elliptic variational problems

Conference · Wed Apr 01 04:00:00 EST 1998

OSTI ID:672012

Hardin, D P ^[1]; Roach, D W ^[2]

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1. Vanderbilt Univ., Nashville, TN (United States). Mathematics Dept.
2. Sandia National Labs., Albuquerque, NM (United States)

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.

• Research Organization: Sandia National Labs., Albuquerque, NM (United States)
• Sponsoring Organization: USDOE Office of Financial Management and Controller, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 672012
• Report Number(s): SAND--98-0975C; CONF-980434--; ON: DE98004760; BR: YB0100000
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
DIFFERENTIAL EQUATIONS
GALERKIN-PETROV METHOD
MATHEMATICAL SPACE
MATRICES
TRANSFORMATIONS
VARIATIONAL METHODS