The Isogeometric Boundary Element Method

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures

“…( 27) and ( 28); (iii) β = 2, I e will be a strongly near-singular integral, i.e. (26). The relative error ε r is used to describe the numerical solution accuracy at a computed point, i.e.…”

“…The Boundary Element Method (BEM) is a powerful and efficient method for solving many engineering problems, offering an alternative to the FEM for a range of engineering simulations, with particular strengths in fracture mechanics, acoustic problems and infinite domain problems [26]. The main advantages of the BEM derive from the fact that its approximations (and mesh) only occur on the boundary, the dimension of the numerical model therefore being one less than that of the physical problem being modelled, and from the high accuracy of its solutions on comparatively coarse meshes.…”

Efficient simulation of inclusions and reinforcement bars with the isogeometric Boundary Element method

“…The previously published iterative method was not suitable to be combined with non-linear iterations. Another novel part is that (in addition to the mapping methods published in [5]) we develop special mapping methods for reinforcement bars and rock bolts. In the following we first establish the governing integral equations and then discuss in detail how the arising volume and surface integrals are evaluated.…”

“…The method was applied to viscous flow in [6,3]. In a recent book published on the isogeometric BEM [5] it was shown how geometrical information can be taken directly from CAD data and that efficient and accurate simulations with very few unknowns can be obtained.…”

Adaptive BEM for elliptic PDE systems, part I: abstract framework, for weakly-singular integral equations

“…Based on a collocation approach, the latter was first considered in [PGK + 09] for 2D and in [SSE + 13] for 3D. We refer to the monograph [BMD20] for an introduction on IGABEM and to [DHK + 18, DHK + 20] for an efficient IGABEM implementation based on the fast multipole method. However, to the best of our knowledge, a posteriori error estimation and adaptive mesh-refinement for IGABEM, have only been considered for simple 2D model problems in the own works [FGP15, FGHP16, FGHP17, FGPS19, GPS20], which employ B-splines on the one-dimensional boundary, and the recent work [FGK + 19], which employs hierarchical B-splines.…”