Abstract
PurposeThis paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.Design/methodology/approachA domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.FindingsApplying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.Originality/valueThe error compared to the standard finite element method is negligible and the computational costs are significantly reduced.
Highlights
In the context of electromagnetic compatibility, ventilation grills are called metascreens (Holloway and Kuester, 2018)
The goal of this work is to improve the computational times in electromagnetic wave simulations by reducing the degrees of freedom
The idea of the Nitsche-type mortaring finite element method for the vector potential wave equation considering non-matching meshes introduced in Hollaus et al (2010) and Heinrich and Nicaise (2001) is altered to fit the quasi-periodic setting with many apertures
Summary
In the context of electromagnetic compatibility, ventilation grills are called metascreens (Holloway and Kuester, 2018). The idea of the Nitsche-type mortaring finite element method for the vector potential wave equation considering non-matching meshes introduced in Hollaus et al (2010) and Heinrich and Nicaise (2001) is altered to fit the quasi-periodic setting with many apertures. The quasi-periodic structure is exploited via a domain decomposition (DD) approach where many of the generated sub-domains are identical The goal is to discretise the exterior domain as coarse as possible such that the wave propagation is appropriately resolved and at the same time discretise the sub-domains fine enough to grasp the local, small-scale behaviour of the solution around the apertures This leads to an upscaling between the solutions on the Xi and the solution on X0.
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