Novel meshless method for solving the potential problems with arbitrary domain

By Der-Liang Young, K. Chen, C. W. Lee. 2005

246 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/7139ada3d3ac22ab4e71b58605097e471f895f8c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Wen Chen
2. Yan Gu
3. Zhuojia Fu
4. Jinyang Zhang
5. Wenzhen Qu
6. Chein-Shan Liu
7. Bozidar Sarler
8. Fei Wang

In Mechanics of Materials

1. Wen Chen
2. Zhuojia Fu
3. Yan Gu
4. Wenzhen Qu
5. Chein-Shan Liu
6. Jinyang Zhang
7. Bozidar Sarler
8. Fei Wang

Citations in the corpus

• Solution of Two-Dimensional Stokes Flow Problems Using Improved Singular Boundary Method (2015, background): “Based on the dependency of the outward normal or tangent vectors on two kernel functions of interior and exterior problems, we can obtain following relationships [17]: ∂ψI(xm,sn) ∂n(sn) =κ ∂ψE(xm,sn) ∂n(sn) , ∂ψI(xm,sn) ∂t(sn) =κ ∂ψE(xm,sn) ∂t(sn) , (2.”
• A new boundary meshfree method with distributed sources (2010, unknown): “[11,13] and Chen et al.”
• A method of fundamental solutions without fictitious boundary (2010, methodology): “On the other hand, it is observed that the error curves of both the SBM and the RMM are decreasing with increasing boundary points, while the SBM converges faster than the RMM.”
• Infinite domain potential problems by a new formulation of singular boundary method (2013, methodology): “According to the dependency of the outward normal vectors on the two kernel functions of interior and exterior problems, we can obtain the following relationships [21]: @u ðxi ;sjÞ @n sj 1⁄4 @u Iðxi ;sjÞ @n sj ; i– j; @u ðxi ;sjÞ @n sj 1⁄4 @u Iðxi ;sjÞ @n sj ; i 1⁄4 j: 8< : ð12Þ”
• A highly accurate collocation Trefftz method for solving the Laplace equation in the doubly connected domains (2008, methodology): “[11] have applied the desingularized boundary integral equation method to the potential problems.”
• Solution of potential flow problems by the modified method of fundamental solutions: Formulations with the single layer and the double layer fundamental solutions (2009, methodology): “This novel method, which essentially represents a sort of blend between BEM and MFS has been originally developed in [19] by using collocation with the double layer Laplace equation fundamental solution.”
• Regularized meshless method for multiply-connected-domain Laplace problems (2006, methodology): “The chosen bases are the doublelayer potentials [18,21,22] as Tðsj ;xiÞ 1⁄4 ðxi sjÞ; nj rij , (6)”
• BOUNDARY PARTICLE METHOD FOR INVERSE CAUCHY PROBLEMS OF INHOMOGENEOUS HELMHOLTZ EQUATIONS (2009, methodology): “To overcome mesh generation problem, facing the traditional mesh-based BEM, a variety of boundary-type meshless methods, in recent years, have been developed and attract a lot of attention, for example, method of fundamental solution (MFS) [4, 11, 22], boundary knot method (BKM) [10], plane wave met”
• A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length (2007, methodology): “The MFS has a broad application in engineering computations, for example, Cho, Golberg, Muleshkov and Li (2004), Hong and Wei (2005), Young, Chen and Lee (2005) , YoungandRuan (2005),and Young,Tsai,Linand Chen (2006).”
• Singular boundary method for modified Helmholtz equations (2014, methodology): “[14] used double-layer fundamental solutions as basis function and proposed regularized meshless method (RMM) for potential problems.”