ParaExp Using Leapfrog as Integrator for High‐Frequency Electromagnetic Simulations. Issue 12 (20th December 2017) - Merkel, M.; Niyonzima, I.; Schöps, S.
Abstract: Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into subintervals and computes the solution on each subinterval in parallel. The overall solution is decomposed into a particular solution defined on each subinterval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique. Key Points: ParaExp using Leapfrog is proposed to parallelly simulate electromagnetic wave problems in time domain Several methods for the approximation of the matrix exponential are discussed Important properties, for example, energy preservation and the performance of the resulting ParaExp scheme, are numerically investigated