Semi-orthogonal wavelets for elliptic variational problems
- Vanderbilt Univ., Nashville, TN (United States). Mathematics Dept.
- 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 Lab. (SNL-NM), 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; TRN: AHC2DT07%%171
- 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
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