high performance computing on graphics processing units: hgpu.org

The Partial Differential Equations (PDEs) play major role in mathematical modeling of problems in engineering and science. The engineering disciplines such as electro-magnetics and fluid dynamics use PDEs heavily and development of products in these engineering fields employs computational intensive numerical methods. These computational intensive methods takes reasonable amount of time on state of the art computers. Nowadays a Graphics Processing Unit (GPU) offers state of the art parallel computing resources and alternative for supercomputing power on desktop computer. In this report various numerical methods for PDEs have been implemented on GPU hardware using NVIDIA’s Compute Unified Device Architecture (CUDA). The simulation of propagation of Gaussian pulse in 2-dimension is implemented on GPU using finite difference time domain method. The computation of eigenvalue and eigenvector involving inverse-iteration, Lanczos and bisection method is implemented on GPU for time dependent Schrodinger equation. The Navier-Stokes equations is solved by finite difference method. Various iterative methods for systems of linear equation in finite difference methods are accelerated on GPU. An unstructured grid based finite volume solver is implemented on GPU. Various optimization and renumbering techniques are employed to achieve the average speed-up of 27x for double precision over CPU implementation.