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On the augmented moving least squares approximation and the localized method of fundamental solutions for anisotropic heat conduction problems

Engineering Analysis with Boundary Elements, 2020
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Li, Xiaolin, Li, Shuling
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Localized method of fundamental solutions for large-scale modelling of three-dimensional anisotropic heat conduction problems – Theory and MATLAB code

Computers & Structures, 2019
Abstract The method of fundamental solutions (MFS) belongs to the family of meshless boundary collocation methods and now has been successfully tried for many kinds of engineering problems. The traditional MFS based on the “global” boundary discretization, however, leads to dense and non-symmetric coefficient matrices that, although smaller in sizes,
Yan Gu   +3 more
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The localized method of fundamental solutions for 2D and 3D second-order nonlinear boundary value problems

Engineering Analysis with Boundary Elements, 2022
Shengdong Zhao   +3 more
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Electroelastic Analysis of Two-Dimensional Piezoelectric Structures by the Localized Method of Fundamental Solutions

Advances in Applied Mathematics and Mechanics, 2023
Summary: Accurate and efficient analysis of the coupled electroelastic behavior of piezoelectric structures is a challenging task in the community of computational mechanics. During the past few decades, the method of fundamental solutions (MFS) has emerged as a popular and well-established meshless boundary collocation method for the numerical ...
Gu, Yan, Lin, Ji, Fan, Chia-Ming
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A Localized Space-Time Method of Fundamental Solutions for Diffusion and Convection-Diffusion Problems

Advances in Applied Mathematics and Mechanics, 2020
Summary: In this paper, a localized space-time method of fundamental solutions (LSTMFS) is proposed to solve the diffusion and convection-diffusion problems. The proposed LSTMFS only requires some arbitrarily-distributed nodes inside the space-time domain and along its boundary.
Wang, Fajie   +3 more
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THE LOCALIZED METHOD OF FUNDAMENTAL SOLUTIONS FOR PLANAR GROUNDWATER FLOW PROBLEMS

SGEM International Multidisciplinary Scientific GeoConference� EXPO Proceedings, 2023
The method of fundamental solutions is a meshless method that belongs to the Trefftz class of numerical methods. The method needs only the boundary to be defined using the set of boundary collocation nodes; it is mathematically effortless to program.
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Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material

Advances in Applied Mathematics and Mechanics, 2023
Summary: This paper documents the first attempt to apply a localized method of fundamental solutions (LMFS) to the acoustic analysis of car cavity containing sound-absorbing materials. The LMFS is a recently developed meshless approach with the merits of being mathematically simple, numerically accurate, and requiring less computer time and storage ...
Chen, Zengtao, Wang, Fajie
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Domain-Decomposition Localized Method of Fundamental Solutions for Large-Scale Heat Conduction in Anisotropic Layered Materials

Advances in Applied Mathematics and Mechanics, 2022
Summary: The localized method of fundamental solutions (LMFS) is a relatively new meshless boundary collocation method. In the LMFS, the global MFS approximation which is expensive to evaluate is replaced by local MFS formulation defined in a set of overlapping subdomains.
Liu, Shuainan, Fu, Zhuojia, Gu, Yan
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A localized meshless collocation method based on fundamental solutions for 3D uncoupled transient thermoelastic problems

International Journal of Heat and Mass Transfer
Linlin Sun   +3 more
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Three-dimensional numerical wave tank containing submerged breakwaters based on the localized method of fundamental solutions

Mathematics and Computers in Simulation
Lanlan Li   +5 more
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