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.
