This contribution shows how these ECE boundary conditions can be implemented into the 3D-finite element method for solving coupled full-wave electromagnetic (EM) field-circuit problems in the frequency domain. Examples are presented on high-frequency Helmholtz and Maxwell problems, in two and three dimensions, to demonstrate the properties of our improvements on parallel computer architectures.Ī natural coupling of a circuit with an electromagnetic device is possible if special boundary conditions, called Electric Circuit Element (ECE), are used for the electromagnetic field formulation. As these modifications still leave some unexploited computational power, we also propose to combine them with right-hand side pipelining to further improve parallelism and achieve significant speed-ups. A notable feature of the new variants is the introduction of partial sweeps that can be performed concurrently in order to make a better usage of the resources. Similarly, the improved preconditioners are based on approximations of the inverse of the Schwarz iteration operator: the general methodology is to apply well-known algebraic techniques to the operator seen as a matrix, which in turn is processed to obtain equivalent matrix-free routines that we use as preconditioners. We propose several improvements to the double-sweep preconditioner originally presented in, which uses sweeping as a matrix-free preconditioner for a Schwarz domain decomposition method. However, an inherent problem with sweeping approaches is the sequential nature of the process, which makes them inadequate for efficient implementation on parallel computers. Sweeping-type algorithms have recently gained a lot of interest for the solution of highfrequency time-harmonic wave problems, in particular when used in combination with perfectly matched layers.
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