Int. J. Numer. Anal. Mod., 11 (2014), pp. 332-345. |
A fully discrete Calderón Calculus for two dimensional time harmonic waves Víctor Domínguez ^{1}, Sijiang Lu ^{2}, Francisco-Javier Sayas ^{2} 1 Departamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 31500, Tudela, España2 Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA Received by the editors October 26, 2012 and, in revised form, March 25, 2013 Abstract In this paper, we present a fully discretized Calderón Calculus for the two dimensional Helmholtz equation. This full discretization can be understood as highly non-conforming Petrov-Galerkin methods, based on two staggered grids of mesh size h, Dirac delta distributions substituting acoustic charge densities and piecewise constant functions for approximating acoustic dipole densities. The resulting numerical schemes from this calculus are all of order h² provided that the continuous equations are well posed. We finish by presenting some numerical experiments illustrating the performance of this discrete calculus. AMS subject classifications: 65N38, 65N35Key words: Calderón calculus, Boundary Element Methods, Dirac deltas distributions, Nyström methods. Email: victor.dominguez@unavarra.es, sjlv@math.udel.edu and fjsayas@math.udel.edu |