Numerical solution of initial-boundary problem for the Helmholtz equation on «discretization – optimization»

Abstract

In this paper we consider the solution of inverse problems on a «discretization — optimization». Considering the direct problem in discrete form, we calculate the functional gradient in a discrete form, using the formula for summation by parts, we obtain the formulation of the conjugate problem in discrete form. Construct an algorithm for solving the inverse problem. Numerically solve the inverse problem. And also performed numerical calculations for the solution of inverse problems.