  In this paper, given a linear system of equations A x = b, we are finding
locations in the plane to place objects such that sending waves from the source
points and gathering them at the receiving points solves that linear system of
equations. The ultimate goal is to have a fast physical method for solving
linear systems. The issue discussed in this paper is to apply a fast and
accurate algorithm to find the optimal locations of the scattering objects. We
tackle this issue by using asymptotic expansions for the solution of the
underlyingpartial differential equation. This also yields a potentially faster
algorithm than the classical BEM for finding solutions to the Helmholtz
equation.
