An isogeometric boundary element method for three-dimensional doubly-periodic layered structures in electromagnetics

Takahashi, Tōru; Hirai, Tetsuro; Isakari, Hiroshi; Matsumoto, Toshiro

doi:10.1016/j.enganabound.2021.11.020

Cited by 9 publications

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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).…”

Section: Application To Be Analysismentioning

confidence: 99%

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

Harmel¹,

Sauer²

2022

Preprint

View full text Add to dashboard Cite

This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature rule (Duffy, 1982) to surface elements containing the singularity and classical Gaussian quadrature to the remaining elements. Two of the four schemes additionally consider a special treatment for elements near to the singularity, where refined Gaussian quadrature and a new moment-fitting quadrature rule are used. The hybrid quadrature schemes are systematically studied on flat B-spline patches and on NURBS spheres considering two different sphere discretizations: An exact single-patch sphere with degenerate control points at the poles and an approximate discretization that consist of six patches with regular elements. The efficiency of the quadrature schemes is further demonstrated in boundary element analysis for Stokes flow, where steady problems with rotating and translating curved objects are investigated in convergence studies for both, mesh and quadrature refinement. Much higher convergence rates are observed for the proposed new schemes in comparison to classical schemes.

show abstract