A node-centered local refinement algorithm for poisson's equation in complex geometries

Journal Article · Tue May 04 04:00:00 EDT 2004 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2004.04.022· OSTI ID:837738

McCorquodale, Peter ^[1]; Colella, Phillip; Grote, David P; Vay, Jean-Luc

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1. LBNL Library

This paper presents a method for solving Poisson's equation with Dirichlet boundary conditions on an irregular bounded three-dimensional region. The method uses a nodal-point discretization and adaptive mesh refinement (AMR) on Cartesian grids, and the AMR multigrid solver of Almgren. The discrete Laplacian operator at internal boundaries comes from either linear or quadratic (Shortley-Weller) extrapolation, and the two methods are compared. It is shown that either way, solution error is second order in the mesh spacing. Error in the gradient of the solution is first order with linear extrapolation, but second order with Shortley-Weller. Examples are given with comparison with the exact solution. The method is also applied to a heavy-ion fusion accelerator problem, showing the advantage of adaptivity.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director. Office of Science. Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing Program, Laboratory Directed Research and Development LBNL, Lawrence Livermore National Laboratory W-7405-ENG-48 (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 837738
• Report Number(s): LBNL--54138; HIFAN 1313
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 201
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
99 GENERAL AND MISCELLANEOUS
ACCELERATORS
ALGORITHMS
BOUNDARY CONDITIONS
EXACT SOLUTIONS
EXTRAPOLATION
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