Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. On secondorderaccurate discretization of 3D interface problems and its fast solution with a pointwise multigrid solver
 IMA journal of numerical analysis 22 (2002), No.3, pp.391406 ISSN: 02724979 ISSN: 14643642 

 English 
 Journal Article 
 Fraunhofer IESE () Fraunhofer ITWM () 
 secondorderaccurate discretization; 3D interface problem; pointwise multigrid solver; 3D elliptic equation; discontinuous coefficient; finite volume discretization; cellcentred grid; multigrid algorithm; Jacobi smoother; illconditioned system; linear algebraic equation; iterative solver; eightcomer problem 
Abstract
This paper is devoted to developing a complete algorithm for solving a class of 3D elliptic equations with discontinuous coefficients (so called interface problems). The algorithm is based on a more accurate discretization of the problem, as well as on an efficient solution of the discretized equations. A new sevenpoint finite volume discretization on cellcentred grids is derived. It is proved that this discretization is secondorder accurate in the discrete W/sub 2//sup 1/ norm. A multigrid algorithm exploiting pointwise a Jacobi smoother is used to solve the illconditioned system of linear algebraic equations arising after the discretization of the above problem. It is demonstrated that the choice of the stopping criterion plays a significant role for the efficiency of the iterative solver. The discretization and the iterative solver are tested in solving an eight comer problem (i.e. with different diffusivity coefficients in eight subregions). Secondorder convergence for both the solution and the flux is observed in numerical experiments. Numerical experiments also demonstrate that the algorithm developed for solving 3D interface problems is robust and fast.