On choosing the location of the sources in the MFS

Chen, C. S.; Karageorghis, Andréas; Li, Yan

doi:10.1007/s11075-015-0036-0

Cited by 151 publications

(59 citation statements)

References 25 publications

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“…They observed that placing the source points on a circle leads to poor results and recommended pseudo boundaries similar to the main boundary of the problem. Chen et al [Chen, Karageorghis and Li (2016)] investigated on the configuration of source points in the MFS for 2D and 3D boundary value problems governed by the Laplace and biharmonic equations. They used an optimization algorithm based on the accuracy of the imposition of boundary conditions for proper determination of the location of source points.…”

Section: Introductionmentioning

confidence: 99%

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Hematiyan¹,

Arezou²,

Dezfouli³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

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In this paper, some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made. First, the effects of the distance between pseudo and main boundaries on the solution are investigated and by a numerical study a lower bound for the distance of each source point to the main boundary is suggested. In some cases, the resulting system of equations becomes ill-conditioned for which, the truncated singular value decomposition with a criterion based on the accuracy of the imposition of boundary conditions is used. Moreover, a procedure for normalizing the shear modulus is presented that significantly reduces the condition number of the system of equations. By solving two example problems with stress concentration, the effectiveness of the proposed methods is demonstrated.

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Section: Introductionmentioning

confidence: 99%

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Hematiyan¹,

Arezou²,

Dezfouli³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

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“…To obtain a promising result of the location of the source points for the proposed method in this study, a sensitivity study was first carried out. An algorithm similar to the study conducted by Chen et al [31] was adopted with scaling of the artificial boundary with the domain size. Assuming the boundary collocation points can be described as a known parametric representation as follows:…”

Section: Validation Of the Proposed Methodsmentioning

confidence: 99%

A Novel Boundary-Type Meshless Method for Modeling Geofluid Flow in Heterogeneous Geological Media

Xiao

Liu

et al. 2018

Geofluids

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A novel boundary-type meshless method for modeling geofluid flow in heterogeneous geological media was developed. The numerical solutions of geofluid flow are approximated by a set of particular solutions of the subsurface flow equation which are expressed in terms of sources located outside the domain of the problem. This pioneering study is based on the collocation Trefftz method and provides a promising solution which integrates the T-Trefftz method and F-Trefftz method. To deal with the subsurface flow problems of heterogeneous geological media, the domain decomposition method was adopted so that flux conservation and the continuity of pressure potential at the interface between two consecutive layers can be considered in the numerical model. The validity of the model is established for a number of test problems. Application examples of subsurface flow problems with free surface in homogenous and layered heterogeneous geological media were also carried out. Numerical results demonstrate that the proposed method is highly accurate and computationally efficient. The results also reveal that it has great numerical stability for solving subsurface flow with nonlinear free surface in layered heterogeneous geological media even with large contrasts in the hydraulic conductivity.

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“…For such problems involving regions of irregular geometry, the use of numerical methods, particularly the boundary-type meshless method, to approximate numerical solutions is advantageous. In the past decades, several meshless methods have been proposed, such as the collocation Trefftz method (CTM) [28][29][30][31], the method of fundamental solutions (MFS) [32][33][34], smoothed particle hydrodynamics (SPH) [35], diffuse element method [36], and the boundary particle method [37]. Among these meshless methods, the CTM can be categorized into the boundary-type meshless method and provides the most accurate solutions with optimal numerical stability [38,39].…”

Section: Introductionmentioning

confidence: 99%

Modeling of Transient Flow in Unsaturated Geomaterials for Rainfall-Induced Landslides Using a Novel Spacetime Collocation Method

Liu

et al. 2018

Geofluids

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The modeling of transient flow in unsaturated soils for rainfall-induced landslides using a novel spacetime collocation method is presented. A numerical solution obtained in the spacetime coordinate system is approximated by superpositioning Trefftz basis functions satisfying the linearized Richards equation for collocation points on the spacetime domain boundary. The Gardner exponential model is adopted to derive the linearized Richards equation to describe the soil-water characteristic curve in unsaturated soils. To deal with the rainfall-induced landslides, the infinite slope stability analysis coupled with the proposed meshless method with the consideration of the fluctuation of time-dependent matric suction is developed. The proposed method is validated for several test problems. Application examples of transient modeling of flow for rainfall-induced landslides in homogenous unsaturated soils are also conducted. Numerical results demonstrate that the proposed method is highly accurate to deal with transient flow in unsaturated soils for rainfall-induced landslides. In addition, it is found that the numerical method using the Richards equation with the Gardner model may provide a promising solution for different soil textures.

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On choosing the location of the sources in the MFS

Cited by 151 publications

References 25 publications

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

A Novel Boundary-Type Meshless Method for Modeling Geofluid Flow in Heterogeneous Geological Media

Modeling of Transient Flow in Unsaturated Geomaterials for Rainfall-Induced Landslides Using a Novel Spacetime Collocation Method

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