A meshless particle method for poisson and diffusion problems with discontinuous coefficients and inhomogeneous boundary conditions

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

  • Nicolas Fiétier - , Swiss Institute of Bioinformatics, ETH Zurich (Autor:in)
  • Ömer Demirel - , Swiss Institute of Bioinformatics, ETH Zurich (Autor:in)
  • Ivo F. Sbalzarini - , Swiss Institute of Bioinformatics, ETH Zurich (Autor:in)

Abstract

We present a meshless particle method for Poisson and diffusion problems on domains with discontinuous coefficients and possibly inhomogeneous boundary conditions. The method is based on a domain-decomposition approach with suitable interface and boundary conditions between regions of different diffusivities, and on using discretization-corrected particle strength exchange operators [B. Schrader, S. Reboux, and I. F. Sbalzarini, J. Comput. Phys., 229 (2010), pp. 4159- 4182]. We propose and compare two methods: The first one is based on an immersed interface approach, where interfaces are determined implicitly using a simplified phase-field equation. The second method uses a regularization technique to transform inhomogeneous interface or boundary conditions to homogeneous ones with an additional continuous volume contribution. After presenting the methods, we demonstrate their capabilities and limitations on several one-dimensional and threedimensional test cases with Dirichlet and Neumann boundary conditions, and both regular and irregular particle distributions.

Details

OriginalspracheEnglisch
Seiten (von - bis)A2469-A2493
FachzeitschriftSIAM journal on scientific computing
Jahrgang35
Ausgabenummer6
PublikationsstatusVeröffentlicht - 2013
Peer-Review-StatusJa
Extern publiziertJa

Externe IDs

ORCID /0000-0003-4414-4340/work/159608285

Schlagworte

Schlagwörter

  • DC-PSE, Diffusion, Discontinuity, Interface condition, Particle method, Poisson equation, PSE operators, Regularization