CONTRIBUTION TO THE NUMERICAL-SOLUTION OF THE LAPLACE AND HEAT-EQUATIONS BY SPECIALIZED HARDWARE

Contribution to the numerical solution of the Laplace and heat equations by specialized hardware. We adapt the classical finite difference method to compute solutions of the Heat and Laplace equations with help from special purpose hardware. Parallelism is achieved through a pipe-line, whose depth can be adapted to available silicon area. An implementation of the method on PAM (Programmable Active Memory) technology runs at 20 MHz, with a pipe depth of 128 operators. This lets us compute 5G additions and shifts per second, with a 24 bits fixed-point data format. Since it is easy to show that fixed-point gives the same results as floating-point for these two problems, this exceeds computing performances previously reported ([McB 88] and [McB & al 91]) for super-computers. A serial computer will need to execute 25 G instructions per second, to reproduce the same computation. The price of solving the Heat and Laplace equations, in $ per operation per second, is two order of magnitude lower with the proposed PAM implementation, than with super-computers.