6533b82afe1ef96bd128cb89

RESEARCH PRODUCT

A generalized finite difference method using Coatmèlec lattices

Miguel Arevalillo-herráezFrancisco R. VillatoroFernando GiménezMiguel A. García-marchPedro Fernández De Córdoba

subject

Finite volume methodPartial differential equationHardware and ArchitectureMesh generationMathematical analysisFinite differenceFinite difference methodGeneral Physics and AstronomyMeshfree methodsFinite difference coefficientFinite element methodMathematics

description

Generalized finite difference methods require that a properly posed set of nodes exists around each node in the mesh, so that the solution for the corresponding multivariate interpolation problem be unique. In this paper we first show that the construction of these meshes can be computerized using a relatively simple algorithm based on the concept of a Coatmelec lattice. Then, we present a generalized finite difference method which provides a numerical solution of a partial differential equation over an arbitrary domain, using the generated meshes. The accuracy and mesh adaptivity of the method is evaluated using elliptical equations in several domains.

yearjournalcountryeditionlanguage
2009-07-01Computer Physics Communications
https://doi.org/10.1016/j.cpc.2009.01.015