Evaluation of FPGA hardware as a new approach for accelerating the numerical solution of the Laplace problem

Abstract:

Nowadays one of the main challenges facing fluid dynamics simulations is the long duration of numerical calculations. Mathematical operations in numerical solution of differential equations using traditional hardware such as CPU, are done in a series of orderly calculations and therefore take a lot of time to complete. A new solution procedure for numerical calculations is presented using FPGA (Field Programmable Gate Arrays) hardware, which will enable parallel processing inside the hardware. The main goal of this research is to use FPGAs instead of CPUs for numerical solution of the Laplace equation and therefore to accelerate its solution. FPGA is an integrated circuit containing a number of logic blocks. The architecture of this hardware can be reprogrammed and configured after manufacturing. So, it’s possible to design and implement complex circuits for various applications using an FPGA. In the present research, first, the ability of FPGAs in mathematical operations on floating point numbers is studied. Then, the Laplace problem is implemented and solved numerically on a specific FPGA hardware using different mesh size and numerical methods. The time duration and precision results of the calculations are compared to the results from a CPU. The calculation procedure on the FPGA is up to twenty times faster than a conventional CPU, with the same data precision. Several numerical and analytical solutions are used to validate the results.

Keywords:

FPGA, CFD, Reconfigurable Hardware, Hardware Definition Language, Accelerating Numerical Solutions.