Mesh sampling and weighting for the hyperreduction of nonlinear Petrov–Galerkin reduced‐order models with local reduced‐order bases
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DOI: 10.1002/nme.6603
Abstract: The energy‐conserving sampling and weighting (ECSW) method is a hyper‐reduction method originally developed for accelerating the performance of Galerkin projection‐based reduced‐order models (PROMs) associated with large‐scale finite element models, when the underlying projected operators need… read more here.
Keywords: order; sampling weighting; petrov galerkin; method ... See more keywords
Mesh Distortion Insensitive and Locking-free Petrov-Galerkin low-order EAS Elements for Linear Elasticity
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DOI: 10.1002/nme.6817
Abstract: One of the most successful mixed finite element methods in solid mechanics is the enhanced assumed strain (EAS) method developed by Simo and Rifai in 1990. However, one major drawback of EAS elements is the… read more here.
Keywords: order; eas elements; distortion; petrov galerkin ... See more keywords
A total Lagrangian, objective and intrinsically locking‐free Petrov–Galerkin SE(3) Cosserat rod finite element formulation
Sign Up to like & getrecommendations! Published in 2023 at "International Journal for Numerical Methods in Engineering"
DOI: 10.1002/nme.7236
Abstract: Based on more than three decades of rod finite element theory, this publication combines the successful contributions found in the literature and eradicates the arising drawbacks like loss of objectivity, locking, path‐dependence and redundant coordinates.… read more here.
Keywords: cosserat rod; rod finite; finite element; petrov galerkin ... See more keywords
Fully Petrov–Galerkin spectral method for the distributed-order time-fractional fourth-order partial differential equation
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DOI: 10.1007/s00366-020-00968-2
Abstract: Distributed fractional derivative operators can be used for modeling of complex multiscaling anomalous transport, where derivative orders are distributed over a range of values rather than being just a fixed integer number. In this paper,… read more here.
Keywords: order; time fractional; petrov galerkin; time ... See more keywords
Numerical simulation of metal removal in laser drilling using meshless local Petrov–Galerkin collocation method
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DOI: 10.1016/j.apm.2017.08.032
Abstract: Abstract A simplified 2D axisymmetric meshfree model of transient metal laser drilling is proposed for a continuous laser beam of Gaussian distribution. The penetration depth is predicted over the whole ablation time. The meshless local… read more here.
Keywords: laser drilling; petrov galerkin; meshless local; metal ... See more keywords
Anisotropic transient thermoelasticity analysis in a two-dimensional decagonal quasicrystal using meshless local Petrov–Galerkin (MLPG) method
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DOI: 10.1016/j.apm.2018.09.024
Abstract: Abstract The meshless local Petrov–Galerkin (MLPG) method is employed for anisotropic transient thermoelasticity analysis of 2D decagonal quasicrystals (QCs) subjected to transient thermal and mechanical shock loadings. The wave type model and the elasto-hydrodynamic model… read more here.
Keywords: mlpg method; method; local petrov; petrov galerkin ... See more keywords
An adaptive meshless local Petrov–Galerkin method based on a posteriori error estimation for the boundary layer problems
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DOI: 10.1016/j.apnum.2016.09.007
Abstract: Abstract A new adaptive moving least squares (MLS) method with variable radius of influence is presented to improve the accuracy of Meshless Local Petrov–Galerkin (MLPG) methods and to minimize the computational cost for the numerical… read more here.
Keywords: petrov galerkin; method; meshless local; based posteriori ... See more keywords
An h-p version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations
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DOI: 10.1016/j.apnum.2019.03.015
Abstract: Abstract We propose and analyze an h-p version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations with vanishing delays. We establish a priori error estimates in the L 2 -… read more here.
Keywords: time; time stepping; version continuous; continuous petrov ... See more keywords
A novel Petrov-Galerkin method for a class of linear systems of fractional differential equations
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DOI: 10.1016/j.apnum.2021.07.012
Abstract: Abstract This paper presents a novel Petrov-Galerkin method for a class of linear systems of fractional differential equations. New fractional-order generalized Jacobi functions are introduced, and their approximation properties are investigated. We show that these… read more here.
Keywords: novel petrov; method; galerkin method; method class ... See more keywords
Peridynamic Petrov–Galerkin method: A generalization of the peridynamic theory of correspondence materials
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DOI: 10.1016/j.cma.2019.112636
Abstract: Abstract The Peridynamic Petrov–Galerkin (PPG) method is a meshfree approach based on the peridynamic integro-differential form of the momentum equation. The spurious oscillations in the common peridynamic correspondence formulation are investigated. They occur due to… read more here.
Keywords: correspondence; ppg method; petrov galerkin; method ... See more keywords
A Petrov-Galerkin finite element method for 2D transient and steady state highly advective flows in porous media
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DOI: 10.1016/j.compgeo.2018.04.013
Abstract: Abstract A new Petrov-Galerkin finite element method for two-dimensional (2D) highly advective flows in porous media, which removes numerical oscillations and retains its precision compared to the conventional Galerkin finite element method, is presented. A… read more here.
Keywords: finite element; element method; galerkin finite; petrov galerkin ... See more keywords