A fast BIE iteration method for an arbitrary body in a flow of incompressible inviscid fluid

The paper is concerned with the new iteration algorithm to solve boundary integral equations arising in boundary value problems of mathematical physics. The stability of the algorithm is demonstrated on the problem of a flow around bodies placed in the incompressible inviscid fluid. With a discrete numerical treatment, we approximate the exact matrix by a certain Töeplitz one and then apply a fast algorithm for this matrix, on each iteration step. We illustrate the convergence of this iteration scheme by a number of numerical examples, both for hard and soft boundary conditions. It appears that the method is highly efficient for hard boundaries, being much less efficient for soft boundaries.