Non-conformal domain decomposition methods for time-harmonic Maxwell equations

Abstract

We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term, are discussed in detail. We address in full the formulations, and subsequently, their applications to problems with significant amounts of repetitions. The non-conformal DDM approach has also been extended into surface integral equation methods. We elucidate a non-conformal integral equation domain decomposition method and a generalized combined field integral equation method for modelling EM wave scattering from non-penetrable and penetrable targets, respectively. Moreover, a plane wave scattering from a composite mockup fighter jet has been simulated using the newly developed multi-solver domain decomposition method.

High performance domain decomposition methods for signal integrity modeling in 3-D interconnects

“…As pointed out in many previous works, the choice of transmission conditions is of vital importance in determining the convergence behavior of the DD method. The use of first order Robin-type TCs in [2] makes the DD iteration converge quickly for propagating eigenmodes, though the evanescent modes fail to converge. Lately, a few higher order TCs have been proposed to improve upon the Robin TC.…”

“…Moreover, as indicated in [2], every outer loop (that is each DD iteration) requires solving each sub-domain matrix equation once. In essence, this is similar to solving the subdomain matrix equation with sequential, multiple right-handsides (RHSs).…”

“…The proposed work has advantages over the existing DD approaches [2], [3] in three aspects: (a) an automatic, adaptive geometry-aware DD method. It starts by decomposing a large, complex geometrical domain into a collection of CAD components (sub-domains), which are discretized independently and concurrently; (b) a flexibly hybrid solution strategy, where volume-based differential equation solvers and surface-based integral solvers can be applied to individual sub-domain problems based on local characteristics; (c) the continuity of the physical quantities across the domain boundaries is enforced through the optimized transmission condition (TC), which leads to quasi-optimal convergence in DD iterations that is provably scalable for multi-scale objects.…”

Accelerated domain decomposition FEM-BEM solver for magnetic resonance imaging (MRI) via discrete empirical interpolation method

“…Double layer cement variable are defined on two sides of Γ 1 , a fictitious surface enclosing domain Ω 1 . A Robin-Type impedance boundary condition is introduced across the interface to connect the two sub-problems and to enforce the continuity of the tangential electromagnetic fields [5]. The governing equations for the interior problem (x ∈ Ω 1 ) are:…”

“…Each subregion is solved by employing the best suited computational electromagnetic technique. The coupling between sub-regions is carried out through Robin-type transmission conditions (Robin TC) that enforce both electric and magnetic field continuity and improve the convergence of the overall iterative solution [5]. In MRI scattering, integral equation (IE) solvers such as boundary element method (BEM) are employed to The computation of the coupling between domains is very time consuming and is the bottleneck in the whole simulation.…”