A spectral element solution of the shallow-water equations on multiprocessor computers

A shallow-water spectral element ocean model is implemented on multiple instruction multiple data, distributed memory parallel computers. A communications-minimizing partitioning algorithm for unstructured meshes, based on graph theory, is presented and is shown to improve the efficiency in a limited range of granularities. A domain decomposition implementation with an architecture-independent communications scheme, using message passing, is devised and rested on an nCUBE/2. a Gray T3D, and an IBM SP2. The implementation exhibits high efficiencies over a wide range of granularities. An order of magnitude analysis shows that, to leading order, the efficiency stays constant when KN2 grows proportionally to P, where K is the total number of elements, N is the order of the spectral truncation within an element, and P is the number of processors.