A Numerical Method for the Problem of Coefficient Identification of the Wave Equation Based on a Local Observation on the Boundary

摘要

The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to a variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.