**Authors:**Jielin Li, Peter Monk, and Daniel S. Weile

**Source:**FERMAT, Articles, 2016-Vol16-Jul_Aug-004

**Abstract: **The use of convolution quadrature (CQ)
approaches for the discretization of time domain integral
equations (TDIEs) is described in full. Using an
operational calculus approach, CQ methods render the
continuous TDIE convolution discrete through a
mapping from the Laplace domain to the Z domain. This
process simplifies the computation of the spatial
integrations needed for the integral equation
discretization, as the shadow region endemic to temporal
Galerkin discretization is eschewed. The underlying
frequency domain nature of CQ also eases its use for
dispersive kernels. Numerical results will demonstrate
the technique.

**Index Terms: **Time domain integral equations (TDIE),
Convolution Quadrature (CQ), marching on in time
(MOT).

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