Using High-Order Transport Theorems for Implicitly Defined Moving Curves to Perform Quadrature on Planar Domains

DOI10.1137/20M1341283zbMath1477.65243OpenAlexW3187703641MaRDI QIDQ5009342

Bert Jüttler, Felix Scholz

Publication date: 20 August 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1341283

zbMATH Keywords

numerical quadraturetrimmingisogeometric analysisfictitious domain methodstransport theoremimmersed methodsunfitted finite element method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Curves in Euclidean and related spaces (53A04) Numerical integration (65D30) Moving boundary problems for PDEs (35R37) Fictitious domain methods for boundary value problems involving PDEs (65N85)

Uses Software

• G+Smo
• CutFEM

Cites Work

• Unnamed Item
• Numerical integration of discontinuities on arbitrary domains based on moment fitting
• The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models
• Numerical integration over implicitly defined domains for higher order unfitted finite element methods
• Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries
• Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons
• Ghost penalty
• \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method
• Isogeometric analysis for trimmed CAD surfaces
• On the volume of sets bounded by refinable functions
• Immersed finite element method
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Geometrically unfitted finite element methods and applications. Proceedings of the UCL workshop, London, UK, January, 6--8, 2016
• An immersed-isogeometric model: application to linear elasticity and implementation with THBox-splines
• On the numerical integration of trimmed isogeometric elements
• A fictitious domain method for Dirichlet problem and applications
• Preconditioning immersed isogeometric finite element methods with application to flow problems
• Isogeometric analysis on V-reps: first results
• Volumetric untrimming: precise decomposition of trimmed trivariates into tensor products
• Explicit dynamic isogeometric B-rep analysis of penalty-coupled trimmed NURBS shells
• Numerical integration on trimmed three-dimensional domains with implicitly defined trimming surfaces
• Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach
• Error-estimate-based adaptive integration for immersed isogeometric analysis
• Numerical integration over implicitly defined domains with topological guarantee
• First order error correction for trimmed quadrature in isogeometric analysis
• Quasi-conforming analysis method for trimmed CAD surfaces
• Adaptively weighted numerical integration in the finite cell method
• Smart octrees: accurately integrating discontinuous functions in 3D
• Improved conditioning of isogeometric analysis matrices for trimmed geometries
• Approximation in FEM, DG and IGA: a theoretical comparison
• Adaptively weighted numerical integration over arbitrary domains
• Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods
• Curvature formulas for implicit curves and surfaces
• Multigrid solvers for immersed finite element methods and immersed isogeometric analysis
• Weighted Extended B-Spline Approximation of Dirichlet Problems
• Unfitted Finite Element Methods Using Bulk Meshes for Surface Partial Differential Equations
• CutFEM: Discretizing geometry and partial differential equations
• Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces
• An Unfitted Hybrid High-Order Method for Elliptic Interface Problems
• An Unfitted Discontinuous Galerkin Method Applied to Elliptic Interface Problems
• The Generation of 3D Trimmed Elements for NURBS-Based Isogeometric Analysis
• A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries
• High-order Numerical Quadratures in a Tetrahedron with an Implicitly Defined Curved Interface
• A Multigrid Method for Unfitted Finite Element Discretizations of Elliptic Interface Problems
• Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
• High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles

This page was built for publication: Using High-Order Transport Theorems for Implicitly Defined Moving Curves to Perform Quadrature on Planar Domains