Higher-order meshing of implicit geometries. I: Integration and interpolation in cut elements
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Publication:2308774
DOI10.1016/j.cma.2016.10.019zbMath1439.65212arXiv1706.00578OpenAlexW2537053663WikidataQ56660219 ScholiaQ56660219MaRDI QIDQ2308774
Publication date: 3 April 2020
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1706.00578
Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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Cites Work
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- 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
- Fictitious domain finite element methods using cut elements. II: A stabilized Nitsche method
- High order X-FEM and levelsets for complex microstructures: uncoupling geometry and approximation
- Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons
- Finite element analysis on implicitly defined domains: an accurate representation based on arbitrary parametric surfaces
- Studied X-FEM enrichment to handle material interfaces with higher order finite element
- Fictitious domain finite element methods using cut elements. I: A stabilized Lagrange multiplier method
- The finite cell method for three-dimensional problems of solid mechanics
- Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
- The weak element method applied to Helmholtz type equations
- Weak-element approximations to elliptic differential equations
- The partition of unity finite element method: basic theory and applications
- An extended finite element method with higher-order elements for curved cracks
- Level set methods and dynamic implicit surfaces
- An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
- Numerical simulation of a cylinder in uniform flow: Application of a virtual boundary method
- An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
- The design and analysis of the generalized finite element method
- A least-squares method for the Helmholtz equation
- Smart octrees: accurately integrating discontinuous functions in 3D
- Geometrically accurate, efficient, and flexible quadrature techniques for the tetrahedral finite cell method
- Higher-order accurate integration for cut elements with Chen-Babuška nodes
- High order unfitted finite element methods on level set domains using isoparametric mappings
- Adaptive embedded/immersed unstructured grid techniques
- Transfinite element methods: Blending-function interpolation over arbitrary curved element domains
- The hp-d -adaptive finite cell method for geometrically nonlinear problems of solid mechanics
- Highly accurate surface and volume integration on implicit domains by means of moment-fitting
- CutFEM: Discretizing geometry and partial differential equations
- Higher-order accurate integration of implicit geometries
- PERFORMANCE OF DIFFERENT INTEGRATION SCHEMES IN FACING DISCONTINUITIES IN THE FINITE CELL METHOD
- The extended/generalized finite element method: An overview of the method and its applications
- Construction of curvilinear co-ordinate systems and applications to mesh generation
- Strong and weak arbitrary discontinuities in spectral finite elements
- On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method
- Higher-order XFEM for curved strong and weak discontinuities
- Fast integration and weight function blending in the extended finite element method
- Development of high-order manifold method
- Elastic crack growth in finite elements with minimal remeshing
- Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- THE PARTITION OF UNITY METHOD
- A Fast Iterative Algorithm for Elliptic Interface Problems
- Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
- New crack‐tip elements for XFEM and applications to cohesive cracks
- An Embedding of Domains Approach in Free Boundary Problems and Optimal Design
- A finite element method for crack growth without remeshing
- High-order extended finite element method for cracked domains
- Global‐local finite element
- Modeling holes and inclusions by level sets in the extended finite element method