Adaptive boundary element methods: a posteriori error estimators, adaptivity, convergence, and implementation
This paper reviews the state of the art and discusses very recent mathematical
developments in the field of adaptive boundary element methods. This includes an overview …
developments in the field of adaptive boundary element methods. This includes an overview …
Adaptive boundary element methods for optimal convergence of point errors
One particular strength of the boundary element method is that it allows for a high-order
pointwise approximation of the solution of the related partial differential equation via the …
pointwise approximation of the solution of the related partial differential equation via the …
[HTML][HTML] Adaptive BEM with inexact PCG solver yields almost optimal computational costs
We consider the preconditioned conjugate gradient method (PCG) with optimal
preconditioner in the frame of the boundary element method for elliptic first-kind integral …
preconditioner in the frame of the boundary element method for elliptic first-kind integral …
[HTML][HTML] ReLU neural network Galerkin BEM
Abstract We introduce Neural Network (NN for short) approximation architectures for the
numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the …
numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the …
[HTML][HTML] Robust coupling of DPG and BEM for a singularly perturbed transmission problem
We consider a transmission problem consisting of a singularly perturbed reaction diffusion
equation on a bounded domain and the Laplacian in the exterior, connected through …
equation on a bounded domain and the Laplacian in the exterior, connected through …
Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations
For the non-preconditioned Galerkin matrix of the hypersingular integral operator, the
condition number grows with the number of elements as well as the quotient of the maximal …
condition number grows with the number of elements as well as the quotient of the maximal …
[HTML][HTML] Functional a posteriori error estimates for boundary element methods
Functional error estimates are well-established tools for a posteriori error estimation and
related adaptive mesh-refinement for the finite element method (FEM). The present work …
related adaptive mesh-refinement for the finite element method (FEM). The present work …
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 …
ReLU neural network Galerkin BEM
A Rubén, H Fernando, S Christoph - 2023 - dlib.phenikaa-uni.edu.vn
We introduce Neural Network (NN for short) approximation architectures for the numerical
solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN …
solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN …
On the coupling of DPG and BEM
We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with
optimal test functions to (i) least-squares boundary elements and (ii) various variants of …
optimal test functions to (i) least-squares boundary elements and (ii) various variants of …