PARALLEL NUMERICAL COMPUTATION: A COMPARATIVE STUDY ON CPU-GPU PERFORMANCE IN PI DIGITS COMPUTATION

As the usage of GPU (Graphical Processing Unit) for non-graphical computation is rising, one important area is to study how the device helps improve numerical calculations. In this work, we present a time performance comparison between purely CPU (serial) and GPU-assisted (parallel) programs in numerical computation. Specifically, we design and implement the calculation of the hexadecimal -digit of the irrational number Pi in two ways: serial and parallel. Both programs are based upon the BBP formula for Pi in the form of infinite series identity. We then provide a detailed time performance analysis of both programs based on the magnitude. Our result shows that the GPU-assisted parallel algorithm ran a hundred times faster than the serial algorithm. To be more precise, we offer that as the value  grows, the ratio between the execution time of the serial and parallel algorithms also increases. Moreover, when  it is large enough, that is This GPU efficiency ratio converges to a constant, showing the GPU's maximally utilized capacity. On the other hand, for sufficiently small enough, the serial algorithm performed solely on the CPU works faster since the GPU's small usage of parallelism does not help much compared to the arithmetic complexity

Efficient p-multigrid spectral element model for water waves and marine offshore structures

In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave-body interaction with high computational efficiency within a single modellingapproach. We design and propose an efficientO(n)-scalable computational procedure based on geometric p-multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high-order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p-multigrid spectralelement model can take advantage of the high-order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h-multigrid approaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of the iterative geometric p-multigrid solver. Results of numerical experiments are presented for wave propagation and for wave-body interaction in an advanced case for focusing design waves interacting with a FPSO. Our study shows, that the use of iterative geometric p-multigrid methods for theLaplace problem can significantly improve run-time efficiency of FNPF simulators.Comment: Submitted to an international journal for peer revie