Numerical method for solving of three-dimensional scattering problems from penetrable body

Summary form only given. We formulate the method of minimal discrepancies for solving some linear equations with a non-self-adjoint operator and prove the theorem which determines the conditions for the convergence of the iterations to the solution. In particular, this method can be applied to solve integral equations with a dissipative operator. Volume integral equations (singular equations for electromagnetic problems and Fredholm equations of the second kind for acoustic problems) which describe three-dimensional scattering problems from penetrable inhomogeneous bodies are considered. With the help of energetic inequalities the feasibility of the iterative method to obtain a solution of such integral equations is demonstrated. To approximate these equations the moment and collocation methods are applied. We prove that the approximate solution converges to the exact solution of the integral equations as the number of basis functions or collocation points tends to infinity. To reduce the computing cost, the direct and inverse discrete Fourier transforms are used. To accelerate the convergence of the iterations to the solution, the multistep minimum-discrepancy method, a generalization of the iterative procedure, is formulated and used.