A computational method to estimate the unknown coefficient in a wave equation using boundary measurements

摘要

The objective of this article is to develop a computational method, which combines an efficient high-order finite difference method for solving wave equation, auto differentiation tools and globally convergent optimization algorithms to estimate the unknown coefficient in a 1-D wave equation. The forward problem is solved by efficient and higher order finite difference methods while the gradient of the cost functional with respect to the coefficient is calculated by an adjoint code which is generated by an auto differentiation tool, such as Tangent linear and Adjoint Model Compiler. Three numerical examples are conducted to demonstrate the effectiveness, robustness and accuracy of the proposed computational method.