A Time-domain Runge-Kutta Dual Reciprocity Boundary Element Method for Scalar Wave Propagation

Abstract In this paper, the dual reciprocity boundary element method combined with the Runge- Kutta method is applied to solve the acoustic radiation problem. In the dual reciprocity scheme, the radial basis function is introduced to transform the equivalent integral equation into an equivalent integral equation of a pure boundary form. After the boundary elements discretization, the second-ordered ordinary differential equations (ODEs) are obtained. Furthermore, these ODEs are transformed into first-order ODEs (Euler equations) by introducing a median variable. The Runge-Kutta method of the fourth order is applied to solve these Euler equations. Two numerical examples of acoustic problems on different structures are presented to illustrate the validity and the accuracy of the proposed method.