Accelerating finite difference time domain simulations with reconfigurable dataflow computers

Abstract

Finite difference methods are widely used, highly parallel algorithms for solving differential equations. However, the algorithms are memory bound and thus difficult to implement efficiently on CPUs or GPUs. In this work we study the implementation of the finite difference time domain (FDTD) method for solving Maxwell's equations on an FPGA-based Maxeler dataflow computer. We evaluate our work with actual problems from the domain of computational nanophotonics. The use of realistic simulations requires us to pay special attention to boundary conditions (Dirichlet, periodic, absorbing), which are critical for the correctness of results but detrimental to the performance and thus frequently neglected. We discuss and evaluate the design of two different FDTD implementations, which outperform CPU and GPU implementations. To our knowledge, our implementation is the fastest FPGA-based FDTD solver.