The Numerical Performance of Wavelets for PDEs: The Multi-Scale Finite Element

Technical Report · Wed Dec 23 04:00:00 EST 1998

OSTI ID:6293837

Christon, M A; Roach, D W

The research summarized in this paper is part of a multiyear effort focused on evaluating the viability of wavelet bases for the solution of partial differential equations. The primary objective for this work has been to establish a foundation for hierarchical/wavelet simulation methods based upon numerical performance, computational efficiency, and the ability to exploit the hierarchical adaptive nature of wavelets. This work has demonstrated that hierarchical bases can be effective for problems with a dominant elliptic character. However, the strict enforcement of orthogonality in the usual L 2 sense is less desirable than orthogonality in the energy norm. This conclusion has led to the development of a multi-scale lineax finite element based on a hierarchical change-of-basis. This work considers the numerical and computational performance of the hierarchical Schauder basis in a Galerkin context. A unique row-column lumping procedure is developed with multi-scale solution strategies for 1-D and 2-D elliptic partial differential equations.

• Research Organization: Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 6293837
• Report Number(s): SAND98-2879J; ON: DE00002792
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990000* -- General & Miscellaneous
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
FUNCTIONS
GALERKIN-PETROV METHOD
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
WAVE FUNCTIONS