Implementation of the Multiscale Stochastic Finite Element Method on Elliptic PDE Problems

Wu, Yue; Xiao, Jianzhuang

doi:10.1142/s0219876217500037

Cited by 9 publications

(3 citation statements)

References 66 publications

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“…Through multi-scale coupling, the influence of the randomness of materials and structures on the overall behavior can be taken into account. Wu and Xiao proposed a multi-scale finite element method to solve a coupled random elliptic PDE problem at two linear scales [25], and applied the multi-scale stochastic finite element method to chloride ion diffusion in a recycled aggregate concrete [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Effect of Micro-Cracks on Chloride Ion Diffusion in Concrete Based on Stochastic Aggregate Approach

Yang,

Wu,

Zhi

et al. 2024

Buildings

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For concrete structures in offshore areas, chloride ion erosion is one of the main factors affecting durability. It is crucial to evaluate the chloride ion permeability resistance of concrete structures. In this paper, a finite element simulation of the chloride ion diffusion process in concrete is conducted. A mass diffusion finite element model based on a random aggregate approach is established to investigate the influences of an aggregate, the interface transition zone, and micro-cracks on the chloride ion diffusion coefficients in concrete. The results show that the mass diffusion finite element analysis based on the exponential function model and the power function model can effectively simulate the chloride ion diffusion process in concrete. In addition, the data reveal that volume fraction and distribution aggregates considerably affect chloride ion diffusivity in concrete. Also, the interface transition zone significantly accelerates chloride ion diffusion in concrete. Moreover, this acceleration effect exceeds the barrier effect of an aggregate.

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Section: Introductionmentioning

confidence: 99%

Effect of Micro-Cracks on Chloride Ion Diffusion in Concrete Based on Stochastic Aggregate Approach

Yang,

Wu,

Zhi

et al. 2024

Buildings

Self Cite

View full text Add to dashboard Cite

show abstract

“…Through multi-scale coupling, the influence of randomness of materials and structures on the overall behavior can be taken into account. Wu and Xiao proposed a multi-scale finite element method to solve a coupled random elliptic PDE problem at two linear scales [24], and applied the multi-scale stochastic finite element method to chloride ion diffusion in recycled aggregate concrete [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Effect of Micro-cracks on Chloride Ion Diffusion in Concrete Based on Stochastic Aggregate Approach

Yang,

Wu,

Zhi

et al. 2024

Preprint

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For concrete structures exposed to offshore areas, chloride ion erosion is one of the main factors affecting the durability. It is crucial to evaluate chloride ion permeability resistance of concrete structures. In this article, a finite element simulation of the chloride ion diffusion process in concrete is conducted. A mass diffusion finite element model based on random aggregate approach is established to investigate the influence of aggregate, interface transition zone, and micro-cracks on chloride ion diffusion coefficients in concrete. The results show that the mass diffusion finite element analysis based on the exponential function model and power function model can effectively simulate the chloride ion diffusion process in concrete. In addition, the data reveal that coarse aggregate is the most important factor affecting chloride ion diffusivity in concrete. However, the interface transition zone significantly accelerates chloride ion diffusion in concrete. Moreover, this acceleration effect exceeds the barrier effect of aggregate.

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“…This has also driven the development of various computational methods. The most well-known among them is the finite element method, one of the most effective methods for solving boundary value problems with partial differential equations as governing equations [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations

Zhi,

Wu,

et al. 2023

Mathematics

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The purpose of this study is to investigate the role that a deep learning approach could play in computational mechanics. In this paper, a convolutional neural network technique based on modified loss function is proposed as a surrogate of the finite element method (FEM). Several surrogate-based physics-informed neural networks (PINNs) are developed to solve representative boundary value problems based on elliptic partial differential equations (PDEs). According to the authors’ knowledge, the proposed method has been applied for the first time to solve boundary value problems with elliptic partial differential equations as the governing equations. The results of the proposed surrogate-based approach are in good agreement with those of the conventional FEM. It is found that modification of the loss function could improve the prediction accuracy of the neural network. It is demonstrated that to some extent, the deep learning approach could replace the conventional numerical method as a significant surrogate model.

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Implementation of the Multiscale Stochastic Finite Element Method on Elliptic PDE Problems

Cited by 9 publications

References 66 publications

Effect of Micro-Cracks on Chloride Ion Diffusion in Concrete Based on Stochastic Aggregate Approach

Effect of Micro-Cracks on Chloride Ion Diffusion in Concrete Based on Stochastic Aggregate Approach

Effect of Micro-cracks on Chloride Ion Diffusion in Concrete Based on Stochastic Aggregate Approach

Surrogate-Based Physics-Informed Neural Networks for Elliptic Partial Differential Equations

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