A new universal numerical technique for the solution of boundary integral equations

Abstract

A new numerical technique for the solution of boundary integral equations is presented, This technique leads to uniquely solvable discretized equations of any mesh and its convergence and rate of convergence do not depend on singularities of kernels of integral equations or boundary geometries, In this sense, this technique is universal. The unique solvability of discretized equations, convergence, and the rate of convergence of the numerical technique are established under only one natural condition of unique solvability of boundary integral equations for any right-hand side.