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Adaptive quadrature/cubature rule: application to polytopes (Q2679485)

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Language	Label	Description	Also known as
English	Adaptive quadrature/cubature rule: application to polytopes	scientific article

Statements

scholarly article

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Adaptive quadrature/cubature rule: application to polytopes (English)

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Nafiseh Niknejadi

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Computer Methods in Applied Mechanics and Engineering

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publication date

20 January 2023

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zbMATH Keywords

numerical integration

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convex and concave polytopes

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moment fitting

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quadrature

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cubature

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1016/j.cma.2022.115726

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Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

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Isogeometric Analysis

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Element‐free Galerkin methods

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A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics

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A fictitious domain method for Dirichlet problem and applications

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Adjusting fictitious domain parameters for fairly priced image-based modeling: application to the regularization of digital image correlation

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Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics

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The finite cell method for three-dimensional problems of solid mechanics

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Towards a general interpolation scheme

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Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations

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A hybrid meshfree discretization to improve the numerical performance of peridynamic models

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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SciANN: a Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks

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An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications

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\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition

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Simple formula for integration of polynomials on a simplex

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High-order quadrature on multi-component domains implicitly defined by multivariate polynomials

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Efficient cut-cell quadrature based on moment fitting for materially nonlinear analysis

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Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

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Quadrature for implicitly-defined finite element functions on curvilinear polygons

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Integration on a convex polytope

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Numerical integration of homogeneous functions on convex and nonconvex polygons and polyhedra

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Fast numerical integration on polytopic meshes with applications to discontinuous Galerkin finite element methods

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An efficient method to integrate polynomials over polytopes and curved solids

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Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery

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Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping

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A finite element method for crack growth without remeshing

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Extended finite element method for three-dimensional crack modelling

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Product Gauss cubature over polygons based on Green's integration formula

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High-Order Quadrature Methods for Implicitly Defined Surfaces and Volumes in Hyperrectangles

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On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method

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Quadrature rules for triangular and tetrahedral elements with generalized functions

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Fast integration and weight function blending in the extended finite element method

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Smart octrees: accurately integrating discontinuous functions in 3D

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Higher-order accurate integration of implicit geometries

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Higher-order meshing of implicit geometries. I: Integration and interpolation in cut elements

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Cut finite element methods for elliptic problems on multipatch parametric surfaces

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Generalized Gaussian quadrature rules on arbitrary polygons

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Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method

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A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions

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A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures

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Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons

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On the numerical integration of trimmed isogeometric elements

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Highly accurate surface and volume integration on implicit domains by means of moment-fitting

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Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods

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An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: application to embedded interface methods

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Adaptively weighted numerical integration over arbitrary domains

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Shape aware quadratures

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Efficient integration method for fictitious domain approaches

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Numerical integration over implicitly defined domains for higher order unfitted finite element methods

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Equivalent polynomials for quadrature in Heaviside function enriched elements

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Equivalent Legendre polynomials: numerical integration of discontinuous functions in the finite element methods

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Numerical integration of discontinuities on arbitrary domains based on moment fitting

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Numerical integration of discontinuous functions: moment fitting and smart octree

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Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting

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Adaptive Integration of Cut Finite Elements and Cells for Nonlinear Structural Analysis

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Selective enrichment of moment fitting and application to cut finite elements and cells

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From geometric design to numerical analysis: a direct approach using the finite cell method on constructive solid geometry

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On the solution of 3D problems in physics: from the geometry definition in CAD to the solution by a meshless method

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On the simulation of image-based cellular materials in a meshless style

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Identifiers

Mathematics Subject Classification ID

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zbMATH DE Number

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10.1016/J.CMA.2022.115726

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Sitelinks

Mathematics(1 entry)

mardi Publication:2679485

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