A coupled isogeometric boundary element and finite element method for electro‐mechanical interaction

Abstract

Solving multiphysical problems is a challenging task in computational engineering both in regard to accuracy and efficiency. Finite element methods (FEM) – while very popular and well established for standard problems – are less straightforward for problems involving interfaces moving due to the influence of external fields. Such problems are characterized by additional challenges, such as mesh dynamics, re‐meshing and possible unboundedness of the external field. The boundary element method (BEM) can help to overcome these challenges. In the BEM formulation, the problem is solved solely from the boundary of the domain. This property – in conjunction with finite element shell and membrane formulations – leads to a very interesting coupled method, requiring only the surface discretization to solve multiphysical interface problems. To show the underling idea of the formulation, the electro‐mechanical interaction between two charged shells is considered as an example.

New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

“…This paper focus on Stokes flow, but the presented quadrature schemes are also applicable to other BE applications like heat transfer (Mera et al, 2002;Zang et al, 2021), acoustics (Amini and Harris, 1990;Venås and Kvamsdal, 2020), elastostatics (Simpson et al, 2012;Taus et al, 2019), mechanical contact (Yac et al, 1970;Zirakashvili, 2020) and electromagnetics (Rajski et al, 2019;Takahashi et al, 2022). The quadrature schemes are further applicable to coupled BE and surface FE formulations that can be used to study droplets (Brown et al, 1980;Sauer, 2014), bubbles (Wang et al, 2003;Boedec et al, 2017), shells (Heltai et al, 2017;Maestre et al, 2017) and wetting (Osman and Sauer, 2015;Luginsland and Sauer, 2017).…”