Time-Dependent Singular Boundary Method for Scalar Wave Equation

This chapter presents a time-dependent singular boundary method for solving two- and three-dimensional scalar wave equations. In contrast with previous chapters focused on frequency domain computation, this chapter focuses on the solution of the scalar wave equation instead of the Helmholtz equation. The timedependent fundamental solution is used here as the basis function. Considering the difference between two- and three-dimensional wave equations, the time-dependent fundamental solution is integrated along with time for solving two-dimensional scalar wave equations. A time-successive evaluation approach without complex mathematical transforms is applied for three-dimensional wave equations.

Keywords: Scalar wave equation, Time-dependent fundamental solution, Timedependent singular boundary method, Origin intensity factor.