مهندسی مکانیک شریف (May 2017)
HARDWARE IMPLEMENTATION OF NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS ON FPGA
Abstract
Nowadays, CPUs and GPUs are used in computations pertaining to numerical solution of differential equations. However, the fixed hardware architecture of CPUs and GPUs makes it difficult to optimally implement many numerical solution algorithms. In recent years, a new method, based on hardware implementation of equations using Field Programmable Gate Array (FPGA), has been given much attention. The unique feature of this approach is the ability to vary the hardware architecture on the basis of the solution algorithm, which results in increased \ solution speed and a reduction in power consumption. This methodology, in which \ hardware can \ vary from one \ architecture to another for computing \ purpose is named \ Reconfigurable Computing (RC). RC can be used to solve a lot of problems such as FEM, FVM with structured or unstructured mesh.In this research, typical problems, such as mass-spring systems and wave equations, have been considered, and hardware implementation on FPGA has been used to solve the resulting differential equations. For modeling these systems, we used the software and hardware which is accessible to us, so we used a domestic FPGA board and MatLab and Xilinx ISE software products. Based on the results, advantages and challenges for hardware implementation of differential equations have been presented. Results for a single element mass-spring system show a comparable solution speed for CPU and FPGA implementation. However, with an increase in the number of elements of the mass-spring system, for example, to 6, the FPGA hardware implementation overtakes CPU and the speed of FPGA becomes almost 8 times that of CPU. Moreover, results of the solution of wave equations show that the speed with FPGA implementation is 3.6 times that of CPU. Therefore, for higher numbers of computational elements, results show the superior process speeds attainable with hardware implementation of equations using FPGA compared to the software mplementation on CPU.
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