A Parallel Performance Study Of The Cartesian Method For Partial Differential Equations On A Sphere

A 3-D Cartesian method for integration of partial differential equations on a spherical surface is developed for parallel computation. The target computer architectures are distributed memory, message passing computers such as the Intel Paragon. The parallel algorithms are described along with mesh partitioning strategies. Performance of the algorithms is considered for a standard test case of the shallow water equations on the sphere. We find the computation times scale well with increasing numbers of processors. - vii - 1. INTRODUCTION The solution of partial differential equations (PDEs) forms the core of many scientific applications. The flow equations in a rotating spherical geometry, for example, are important to weather and climate modeling. This report describes a new method for solving PDEs on a spherical domain and a parallel algorithm implementing the method on a massively parallel computer. The use of triangular meshes for the solution of PDEs on a spherical domain is at..