Tensorial Basis Spline Collocation Method for Poissonʹs Equation

This paper aims to describe the tensorial basis spline collocation method applied to Poissonʹs 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(h4) and O(h6) 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 Poissonʹs equation on a 2563 non-uniform 3D Cartesian mesh by using 128 T3E-750 processors. This represents 215 Mflops per processors.