Forward modeling of gravitational fields on hybrid multi-threaded cluster

Abstract

The analytic solution of the gravimetric tensor components, making use of the gravitational potential equation for a three-dimensional volumetric assembly composed of unit prisms of constant density, demands a high computational cost. This is due to the gravitational potential of each one of these prisms must be calculated for all of the points of a previously defined observation grid, which turns out in a large scale computational cost. In this work we introduce a hybrid design and its parallel implementation, based on OpenMP and MPI, for the calculation of the vectorial components of the gravimetric field and the components of the gravimetric tensor. Since the computing time is drastically reduced, the obtained performance leads close to optimal speed-up ratios. The applied parallelization technique consists of decomposing the problem into groups of prisms and using different memory allocations per processing core to avoid bottleneck issues when accessing the main memory in one cluster node, which are generally produced when using too many execution threads over the same region in OpenMP. Due OpenMP can be only used on shared memory systems is necessary to use MPI for the calculation distribution among cluster nodes, giving as a result a hybrid code (OpenMP+MPI) highly efficient and with a nearly perfect speed-up. Additionally the numerical results were validated with respect to its sequential counterpart.