Numerical solution of initial boundary-value problem for homogeneous wave equation with dynamic boundary conditions using Laguerre transform on time variable and boundary element method

Abstract

Initial boundary-value problem for the homogeneous wave equation with dynamic boundary condition is considered in three-dimensional Lipschitz domain. The Kirchhoff's formula is used to represent the solution and the problem is reduced to time-domain boundary integral equations (TDBIEs) that contain Cauchy data as unknown values. By applying the Laguerre transform, the sequence of systems of boundary integral equations (BIEs) is obtained. It depends only on spatial variables. Besides, it is proved that matrix operator composed with boundary operators corresponding to retarded single layer and double layer potentials is elliptic in special functional space. This property is the basis for the development of the efficient numerical method as composition of the Laguerre transform and boundary element method. The results of numerical experiments for model problems with dynamic boundary conditions demonstrate the dependency of solution on impedance parameter change. In addition, error and estimated order of convergence confirm the correctness and efficiency of proposed approach.