Fast Multipole Time Domain Algorithm for the Scalar and Vector Wave Equation

This paper presents a new algorithm, fast multipole time domain (FMTD), to speed up the evaluation of interactions in the boundary integral equation method for wave equations. In FMTD, the bandlimited source signal in the time marching solution is truncated and converted to frequency domain. The static and dynamic (multilevel) fast multipole method are employed to accelerate the evaluation at discrete frequencies. Finally, the results are transformed back to obtain the transient fields. The numerical results demonstrate the accuracy of FMTD.