Parallelization of an Object-Oriented Unstructured Aeroacoustics Solver

Abstract. A computational aeroacoustics code based on the discontinuous Galerkin method is portedto several parallel platforms using MPI. The discontinuous Galerkin method is a compact high-order methodthat retains its accuracy and robustness on non-smooth unstructured meshes. In its semi-discrete form, thediscontinuous Galerkin method can be combined with explicit time marching methods making it well suitedto time accurate computations. The compact nature of the discontinuous Galerkin method also makes itwell suited for distributed memory parallel platforms. The original serial code was written using an object-oriented approach and was previously optimized for cache-based machines. The port to parallel platformswas achieved simply by treating partition boundaries as a type of boundary condition. Code modificationswere minimal because boundary conditions were abstractions in the original program. Scalability resultsare presented for the SGI Origin, IBM SP2, and clusters of SGI and Sun workstations. Slightly superlinearspeedup is achieved on a fixed-size problem on the Origin, due to cache effects.Key words, discontinuous Galerkin method, object-oriented, unstructured grids, Euler equations, high-order accuracy, superlinear speedupSubject classification. Computer Science1. Motivation. Computational Aeroacoustics (CAA) involves the direct simulation of sound generationand/or propagation about an aircraft or an aircraft component. To be of practical value in the aircraft designprocess, these massive computations must be performed quickly, and to do so requires efficient use of parallelcomputer platforms.CAA methods must provide both temporal and spatial accuracy beyond what the second-order discretiza-tions employed in most other areas of computational aerodynamics are capable of providing. In addition,such methods must be easy to apply to complex geometries without sacrifice of accuracy or robustness.These requirements further complicate the design of the parallel implementation. For instance, traditionalhigh-order finite-difference methods are not compact and the amount of data that must be moved acrosspartition boundaries increases considerably with the order of the method. The requirement for time accuracymeans all partitions must be advanced in lock step. Common techniques used in steady calculations, suchas lagging some information or communicating only after several iterations, cannot be employed.The discontinuous Calerkin method is a relatively new approach that satisfies the numerical requirementsof CAA and the algorithmic requirements of parallel implementation. Discontinuous Galerkin is a compact