Wavelet bases factorization of the heat kernel and associated fast matrix algorithms. (Factorisation sur bases d’ondelettes du noyau de la chaleur et algorithmes matriciels rapides associés.) (French. Abridged English version) Zbl 0822.65072

Charton, Philippe; Perrier, Valérie

C. R. Acad. Sci., Paris, Sér. I 320, No. 8, 1013-1018 (1995).

Summary: We introduce a numerical method to solve the two-dimensional heat and Poisson equations, based on a factorization of the heat kernel on tensorial wavelet bases. The scheme is implicit and is based on fast matrix-matrix products associated with a time acceleration, thanks to the wavelet decomposition properties. The method is validated by numerical tests.

MSC:

65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65F30	Other matrix algorithms (MSC2010)
35K05	Heat equation

Keywords:

heat equation; Poisson equations; tensorial wavelet bases; fast matrix- matrix products; wavelet decomposition; numerical tests