Solving a Poisson Equation with Singularities
by the Least-Squares Collocation Method

Belyaev, Vasily

doi:10.1134/s1995423920030027

Cited by 3 publications

(1 citation statement)

References 5 publications

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“…For this purpose, the hp-version of the least-squares collocation (LSC) method is constructed, where piecewise polynomial functions are used to approximate solution [15,16]. The polynomials degree and grid refinement can be varied easily before running the program.…”

Section: Numerical Iplementation Of the Mathematical Modelmentioning

confidence: 99%

Modelling and Simulation of Deformation and Failure of Reinforced Concrete Beams under Four-Point Bending

Belyaev¹

2021

J. Sib. Fed. Univ., Math. phys.

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A new mathematical model for the four-point bending of reinforced concrete beams is developed and investigated. The model takes into account multi-modulus concrete behavior, nonlinear stress-strain relationships, and damage evolution. An algorithm for a numerical implementation of the model is proposed. The corresponding boundary value problem is solved by the hp-version of the least-squares collocation method in combination with an acceleration of an iterative process based on Krylov subspaces and parallelizing. Special attention is given to the influence of mathematical model parameters on the results of numerical simulation. The results are compared with experimental data and three-dimensional simulation. A satisfactory agreement is shown

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Section: Numerical Iplementation Of the Mathematical Modelmentioning

confidence: 99%

Modelling and Simulation of Deformation and Failure of Reinforced Concrete Beams under Four-Point Bending

Belyaev¹

2021

J. Sib. Fed. Univ., Math. phys.

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Numerical Modelling of Mean-Field Game Epidemic

Neverov,

Krivorotko

2023

Lecture Notes in Computer Science

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ReLU artificial neural networks for the grid adaptation in finite element method

Chen

2021

J. Phys.: Conf. Ser.

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In this paper, we study the rectified linear unit (ReLU) artificial neural network (ANN) for grid adaptation in finite element method, which is used for solving differential equations (DEs) with initial/boundary condition. Compared with the classical adaptive finite element method (AFEM), ReLU ANN based on finite element method can keep the number of grid-points constant but change their relative location. Our numerical experiments show that approximate solutions obtained from the classical finite element method by ReLU ANN are more accurate than those obtained by AFEM.

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Solving a Poisson Equation with Singularities by the Least-Squares Collocation Method

Cited by 3 publications

References 5 publications

Modelling and Simulation of Deformation and Failure of Reinforced Concrete Beams under Four-Point Bending

Modelling and Simulation of Deformation and Failure of Reinforced Concrete Beams under Four-Point Bending

Numerical Modelling of Mean-Field Game Epidemic

ReLU artificial neural networks for the grid adaptation in finite element method

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