TIME-DOMAIN BEM ANALYSIS FOR THE 2D SCALAR WAVE EQUATION: INITIAL CONDITIONS CONTRIBUTIONS TO SPACE AND TIME DERIVATIVES

The complete expressions corresponding to space and time derivatives of Volterra’s integral representation of the time-dependent scalar wave equation are presented in this paper. The concept of finite part of an integral is used in order to compute boundary kernels contributions. Time integration of boundary kernels is performed analytically for linear and constant time approximations for the potential and its normal derivative, respectively. The new integral representations presented in this text are quite general, as contributions due to the initial conditions have also been included. Two examples are presented in order to assess the accuracy of the formulation.