A time domain boundary element method (TDBEM) gives us another possibility of time domain microwave simulations in addition to a finite difference time domain (FDTD) method. In particular, the TDBEM has good advantages in analysis of coupling problems with charged particle motion such as in a particle accelerator. However, it is known that time domain microwave simulations in the particle accelerator by the conventional TDBEM often encounter numerical instability and inaccuracy because of its bad matrix property. To avoid the numerical instability and inaccuracy caused by the conventional open boundary problem formulation of the TDBEM, an initial value problem formulation of 3-D TDBEM is presented in this paper.
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