ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations
This paper applies an existing parallel-in-time method to a specific domain (electromagnetic simulations), offering moderate speedups for practitioners.
ParaExp, a parallel time integration method for linear hyperbolic problems, is applied to electromagnetic wave simulations using Leapfrog integration. Numerical tests on a toy problem and a realistic spiral inductor model show speedups of up to 4x compared to sequential Leapfrog.
Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a particular solution defined on each sub-interval 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.