The effect of quadrature rules on finite element solutions of Maxwell variational problems. Consistency estimates on meshes with straight and curved elements
Sign Up to like & getrecommendations! Published in 2021 at "Numerische Mathematik"
DOI: 10.1007/s00211-021-01186-8
Abstract: We study the effects of numerical quadrature rules on error convergence rates when solving Maxwell-type variational problems via the curl-conforming or edge finite element method. A complete {\em a priori} error analysis for the case… read more here.
Keywords: finite element; quadrature; effect quadrature; rules finite ... See more keywords
Generation and application of multivariate polynomial quadrature rules
Sign Up to like & getrecommendations! Published in 2017 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2018.04.009
Abstract: Abstract The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play… read more here.
Keywords: polynomial quadrature; quadrature; generation application; application multivariate ... See more keywords
Superconvergent isogeometric analysis of natural frequencies for elastic continua with quadratic splines
Sign Up to like & getrecommendations! Published in 2019 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2019.01.010
Abstract: Abstract A superconvergent isogeometric formulation is presented to accurately analyze the natural frequencies for elastic continua. This formulation is realized by a set of superconvergent quadrature rules which are designed for the numerical integration of… read more here.
Keywords: frequencies elastic; quadrature; natural frequencies; elastic continua ... See more keywords
Quadrature rules for isogeometric shell formulations: Study using a real-world application about metal forming
Sign Up to like & getrecommendations! Published in 2020 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2020.112904
Abstract: Abstract This paper studies quadrature rules for simulating large deformations of shells using isogeometric analysis. Several recently proposed rules and their effects on a real-world application known as incremental sheet forming are investigated. It is… read more here.
Keywords: quadrature rules; world application; real world;
Quadrature formulas based on spline quasi-interpolation for hypersingular integrals arising in IgA-SGBEM
Sign Up to like & getrecommendations! Published in 2020 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2020.113441
Abstract: Abstract In this paper, we study the construction of quadrature rules for the approximation of hypersingular integrals that occur when 2D Neumann or mixed Laplace problems are numerically solved using Boundary Element Methods. In particular… read more here.
Keywords: quadrature; spline quasi; hypersingular integrals; quasi interpolation ... See more keywords
On the construction of quadrature rules for Laplace transform inversion
Sign Up to like & getrecommendations! Published in 2017 at "Computational Mathematics and Mathematical Physics"
DOI: 10.1134/s0965542517110094
Abstract: For Laplace transform inversion, a method for constructing quadrature rules of the highest degree of accuracy based on an asymptotic distribution of roots of special orthogonal polynomials on the complex plane is proposed. read more here.
Keywords: quadrature rules; transform inversion; laplace transform; construction quadrature ... See more keywords
A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Models and Methods in Applied Sciences"
DOI: 10.1142/s0218202521500317
Abstract: The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak… read more here.
Keywords: finite element; euclidean balls; element methods; cookbook approximating ... See more keywords
Quadrature Rules for the Fm-Transform Polynomial Components
Sign Up to like & getrecommendations! Published in 2022 at "Axioms"
DOI: 10.3390/axioms11100501
Abstract: The purpose of this paper is to reduce the complexity of computing the components of the integral Fm-transform, m≥0, whose analytic expressions include definite integrals. We propose to use nontrivial quadrature rules with nonuniformly distributed… read more here.
Keywords: quadrature; rules transform; transform polynomial; quadrature rules ... See more keywords