We propose to use a hybrid analog-digital electronic computer to solve partial differential equations (PDEs) arising in scientific simulations and high performance computing (HPC). The simulation of PDEs has extensive applications in commerce, research, and defense. Analog computation potentially decreases the time and energy needed to reach a solution by providing an ability to carry out iterative numerical methods in parallel, and with an infinitesimal time step. Specifically, we investigate the scalability of using analog techniques to accelerate solving elliptic PDEs using multigrid algorithms defined on structured grids. This proposal will evaluate whether speeding up the solution of elliptic PDEs and other numerical kernels would significantly improve overall HPC application speed and efficiency. Any proven improvement in computing hardware and software for these problems, in terms of solution time, energy needed to reach a solution, reliability of obtaining a solution, or generality of the problems that can be solved, would have widespread benefits in understanding of systems modeled using PDEs.
