Abstract
In this paper we describe a realization of a Wavelet–Galerkin method for numerically solving second order elliptic PDEs on general domains using the Wavelet Element Method (WEM) [4, 5]. Suitable C++ data structures allowing an efficient implementation of this method are described and numerical results also indicating the flexibility of our realization are presented.
Similar content being viewed by others
REFERENCES
Berrone, S., and Emmel, L. (2001). A Realization of a Wavelet Galerkin Method on Non-Trivial Domains, Dipartimento di Matematica, Politecnico di Torino, Preprint No. 33.
Berrone, S., and Urban, K. Adaptive wavelet Galerkin methods on distorted domains: Setup of the algebraic system. In Cohen, A., Rabut, C., and Schumaker, L. L. (eds.), Curve and Surface Fitting: Saint-Malo 1999, Vanderbilt University Press, Nashville, Tennessee, pp. 65–74.
Bertoluzza, S., Canuto, C., and Urban, K. (2000). On the adaptive computation of integrals of wavelets. Appl. Numer. Math. 34, 13–38.
Canuto, C., Tabacco, A., and Urban, K. (1999). The wavelet element method, Part I: Construction and analysis. Appl. Comp. Harm. Anal. 6, 1–52.
Canuto, C., Tabacco, A., and Urban, K. (2000). The wavelet element method, Part II: Realization and additional features in 2D and 3D. Appl. Comp. Harm. Anal. 8, 123–165.
Cohen, A., Daubechies, I., and Vial, P. (1993). Wavelets on the interval and fast wavelet transform. Appl. Comp. Harm. Anal. 1, 54–81.
Cohen, A., and Masson, R. (2000). Wavelet Adaptive Method for second order elliptic problems-boundary conditions and domain decomposition. Numer. Math. 86, 193–238.
Dahmen, W. (2001). Wavelet methods for PDEs-Some recent developments. J. Comput. Appl. Math. 128, 133–185.
Dahmen, W., Kunoth, A., and Urban, K. (1999). Biorthogonal spline wavelets on the interval-Stability and moment conditions. Appl. Comp. Harm. Anal. 6, 132–196.
Dahmen, W., and Schneider, R. (1999). Composite wavelets bases for operator equations. Math. Comput. 68, 1533–1567.
Emmel, L. (2000). A C++ Wavelet Library-Version 0.1, Dipartimento di Matematica, Politecnico di Torino, Preprint No. 30.
Gordon, W., and Hall, C. (1973). Transfinite element methods: blending-function interpolation over arbitrary curved element domains. Numer. Math. 21, 109–129.
Grivet-Talocia, S., and Tabacco, A. (2000). Wavelets on the interval with optimal localization. M 3 AS 10, 441–462.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Berrone, S., Emmel, L. Towards a Realization of a Wavelet Galerkin Method on Non-Trivial Domains. Journal of Scientific Computing 17, 307–317 (2002). https://doi.org/10.1023/A:1015278419974
Issue Date:
DOI: https://doi.org/10.1023/A:1015278419974