Adaptive isogeometric boundary element methods with local smoothness control
From MaRDI portal
Publication:5112025
DOI10.1142/S0218202520500074OpenAlexW3100460938WikidataQ114072933 ScholiaQ114072933MaRDI QIDQ5112025
Dirk Praetorius, Stefan Schimanko, Gregor Gantner
Publication date: 27 May 2020
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1903.01830
convergenceboundary element methodadaptive algorithmoptimal convergence ratesisogeometric analysisIGABEMhyper-singular integral equation
Numerical computation using splines (65D07) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Complexity and performance of numerical algorithms (65Y20) Boundary element methods for boundary value problems involving PDEs (65N38)
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Cites Work
- Unnamed Item
- Unnamed Item
- Axioms of adaptivity
- A two-dimensional isogeometric boundary element method for elastostatic analysis
- Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations
- From computer aided design to wavelet BEM
- Isogemetric analysis and symmetric Galerkin BEM: a 2D numerical study
- Nonsingular isogeometric boundary element method for Stokes flows in 3D
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Boundary integral equations
- Adaptive 2D IGA boundary element methods
- Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations
- Fast isogeometric boundary element method based on independent field approximation
- Residual-based a posteriori error estimate for hypersingular equation on surfaces
- Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation
- Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
- Isogeometric symmetric Galerkin boundary element method for three-dimensional elasticity problems
- Evaluation of hypersingular and nearly singular integrals in the isogeometric boundary element method for acoustics
- A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems
- Efficient assembly based on B-spline tailored quadrature rules for the IgA-SGBEM
- Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation
- Energy norm based error estimators for adaptive BEM for hypersingular integral equations
- Adaptive boundary element methods with convergence rates
- Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems
- An application of fast multipole method to isogeometric boundary element method for Laplace equation in two dimensions
- Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence
- Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method
- Numerical Approximation Methods for Elliptic Boundary Value Problems
- Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary elements methods. Part I. The two-dimensional case
- Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines
- Adaptive isogeometric methods with hierarchical splines: Optimality and convergence rates
- Isogeometric Analysis
- Finite elements on degenerate meshes: inverse-type inequalities and applications
- Mathematical analysis of variational isogeometric methods
- Adaptive coupling of boundary elements and finite elements
- Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
- Local inverse estimates for non-local boundary integral operators
- Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods
- Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind
- An a posteriori error estimate for a first-kind integral equation
- Boundary Element Methods
