A framework for developing an FPGA based coprocessor for accelerating numerical computations

In recent years, capability of FPGA hardware for accelerating the solution of differential equations has attracted wide attention. However, complexities associated with the implementation and development of these equations on FPGA has precluded the wider application of this hardware among the users in the field of CFD. In this research, a software framework has been developed, which enables users to develop an FPGA based coprocessor for solving implicit PDE equations, quickly and with minimum complexity. Using this framework, the user defines the solution network and the algebraic equations, and the framework manages other operations such as construction of the solver IP, interface between the CPU and the coprocessor, memory layers and links among various parts. The framework consists of different sections for defining the architecture of the coprocessor using HLS and VIVADO software, and the links with CPU consisting of operating system drivers and operational functions for adjusting initial and boundary conditions and receiving the results through the PCIe port. Simplicity of the developed framework has been demonstrated by the construction of a coprocessor for solving two-dimensional Laplace equation. Comparison of speed of solution on CPU with the FPGA based coprocessor shows a 22-fold increase in the speed of solution of Laplace equation, and if fixed point operation is used in the construction of the coprocessor, the speed will even increase 65-fold.