Tensorial Basis Spline Collocation Method for Poisson's Equation

✍ Scribed by Laurent Plagne; Jean-Yves Berthou

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 134 KB
• Volume: 157
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1999.6338

✦ Synopsis

This paper aims to describe the tensorial basis spline collocation method applied to Poisson's equation. In the case of a localized 3D charge distribution in vacuum, this direct method based on a tensorial decomposition of the differential operator is shown to be competitive with both iterative BSCM and FFT-based methods. We emphasize the O(h 4 ) and O(h 6 ) convergence of TBSCM for cubic and quintic splines, respectively. We describe the implementation of this method on a distributed memory parallel machine. Performance measurements on a Cray T3E are reported. Our code exhibits high performance and good scalability: As an example, a 27 Gflops performance is obtained when solving Poisson's equation on a 256 3 non-uniform 3D Cartesian mesh by using 128 T3E-750 processors. This represents 215 Mflops per processors.