A time-domain Runge-Kutta dual reciprocity boundary element method for scalar wave propagation problem

This paper presents a combined approach utilizing the dual reciprocity boundary element method (DRBEM) and the fourth-order Runge-Kutta method (RKM) to address acoustic radiation problems. Within the dual reciprocity framework, a radial basis function (RBF) is introduced to convert the domain integral into a boundary integral form. Following boundary element discretization, a system of second-order ordinary differential equations (ODEs) is derived. These are subsequently transformed into a set of first-order ODEs (Euler equations) via the introduction of an intermediate variable. The fourth-order Runge-Kutta method is then employed to numerically integrate the resulting system. The validity and accuracy of the proposed method are demonstrated through two numerical examples involving acoustic wave propagation in different structural domains.