Mathematical foundations of adaptive isogeometric analysis
This paper reviews the state of the art and discusses recent developments in the field of
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …
adaptive isogeometric analysis, with special focus on the mathematical theory. This includes …
[HTML][HTML] Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations
We consider the Galerkin boundary element method (BEM) for weakly-singular integral
equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator …
equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator …
Adaptive 2D IGA boundary element methods
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA
boundary element methods for weakly singular integral equations of the first-kind in 2D …
boundary element methods for weakly singular integral equations of the first-kind in 2D …
Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
In a recent work (Feischl et al. in Eng Anal Bound Elem 62: 141–153, 2016), we analyzed a
weighted-residual error estimator for isogeometric boundary element methods in 2D and …
weighted-residual error estimator for isogeometric boundary element methods in 2D and …
[HTML][HTML] Adaptive BEM for elliptic PDE systems, part II: Isogeometric analysis with hierarchical B-splines for weakly-singular integral equations
G Gantner, D Praetorius - Computers & Mathematics with Applications, 2022 - Elsevier
We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical
B-splines for weakly-singular boundary integral equations. We prove that the employed …
B-splines for weakly-singular boundary integral equations. We prove that the employed …
Optimal adaptivity for splines in finite and boundary element methods
G Gantner - 2017 - repositum.tuwien.at
Since the advent of isogeometric analysis (IGA) in 2005, the finite element method (FEM)
and the boundary element method (BEM) with splines have become an active field of …
and the boundary element method (BEM) with splines have become an active field of …
Stable Implementation of Adaptive IGABEM in 2D in MATLAB
G Gantner, D Praetorius, S Schimanko - Computational Methods in …, 2022 - degruyter.com
We report on the Matlab program package IGABEM2D which provides an easily accessible
implementation of adaptive Galerkin boundary element methods in the frame of …
implementation of adaptive Galerkin boundary element methods in the frame of …
Adaptive isogeometric boundary element methods with local smoothness control
G Gantner, D Praetorius… - Mathematical Models and …, 2020 - World Scientific
In the frame of isogeometric analysis, we consider a Galerkin boundary element
discretization of the hyper-singular integral equation associated with the 2D Laplacian. We …
discretization of the hyper-singular integral equation associated with the 2D Laplacian. We …
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
We define and analyze (local) multilevel diagonal preconditioners for isogeometric
boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly …
boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly …
Non-symmetric isogeometric FEM-BEM couplings
M Elasmi, C Erath, S Kurz - Advances in Computational Mathematics, 2021 - Springer
We present a coupling of the Finite Element and the Boundary Element Method in an
isogeometric framework to approximate either two-dimensional Laplace interface problems …
isogeometric framework to approximate either two-dimensional Laplace interface problems …