The numerical performance of wavelets and reproducing kernels for PDE`s
The results presented here constitute a brief summary of an on-going multi-year effort to investigate hierarchical/wavelet bases for solving PDE`s and establish a rigorous foundation for these methods. A new, hierarchical, wavelet-Galerkin solution strategy based upon the Donovan-Geronimo-Hardin-Massopust (DGHM) compactly-supported multi-wavelet is presented for elliptic partial differential equations. This multi-scale wavelet-Galerkin method uses a wavelet transform to yield nearly mesh independent condition numbers for elliptic problems as opposed to the multi-scaling functions that yield condition numbers which increase as the square of the mesh size. In addition, the results of von Neumann analyses for the DGHM multi-wavelet element and the Reproducing Kernel Particle Method (RKPM) are presented for model hyperbolic partial differential equations. RKPM exhibits excellent dispersion characteristics using a consistent mass matrix with the proper choice of refinement parameter and mass matrix formulation. In comparison, the wavelet-Galerkin formulation using the DGHM element delivers a frequency response comparable to a Bubnov-Galerkin formulation with a quadratic element.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Financial Management and Controller, Washington, DC (United States)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 666166
- Report Number(s):
- SAND--98-0107C; CONF-981009--; ON: DE98007160; BR: YN0100000
- Country of Publication:
- United States
- Language:
- English
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