Open Access
ABSTRACT
Chein-Shan Liu1
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 57-68, 2007, DOI:10.3970/icces.2007.003.057
Abstract A new method is developed to solve the interior and exterior Dirichlet problems for the two-dimensional Laplace equation, namely the meshless regularized integral equation method (MRIEM), which consists of three parts: Fourier series expansion, the second kind Fredholm integral equation and an analytically regularized solution of the unknown boundary condition on an artificial circle. We find that the new method is powerful even for the problem with very complex boundary shape and with boundary noise. More >
Open Access
ABSTRACT
Chih-Wen Chang1, Chein-Shan Liu2, Jiang-Ren Chang1
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 69-80, 2007, DOI:10.3970/icces.2007.003.069
Abstract By using a quasi-boundary regularization we can formulate a two-point boundary value problem of the backward heat conduction equation. The ill-posed problem is analyzed by using the semi-discretization numerical schemes. Then, the
resulting ordinary differential equations in the discretized space are numerically
integrated towards the time direction by the Lie-group shooting method to find the
unknown initial conditions. The key point is based on the erection of a one-step
Lie group element G(T) and the formation of a generalized mid-point Lie group
element G(r). Then, by imposing G(T) = G(r) we can seek the missing initial
conditions through a minimum… More >
Open Access
ABSTRACT
R. Schaback1
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 81-86, 2007, DOI:10.3970/icces.2007.003.081
Abstract This is a short summary of recent mathematical results on error bounds and convergence of certain unsymmetric methods, including variations of Kansa's collocation technique and Atluri's MLPG method. The presentation is kept as simple as possible in order to address a larger community working on applications in Science and Engineering. More >
Open Access
ABSTRACT
J. Sladek1, V. Sladek1, Ch. Zhang2, C.L. Tan3
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 87-92, 2007, DOI:10.3970/icces.2007.003.087
Abstract In this paper, the Meshless Local Petrov-Galerkin (MLPG) method for two-dimensional (2-d), linear and transient coupled thermoelastic analysis in orthotropic solids is presented. To eliminate the time-dependence in the governing equations, the Laplace-transform technique is used. Local integral equations are derived for small circular sub-domains which surround nodal points distributed over the analyzed domain. As for the spatial variations of the displacements and temperature, they are approximated by the Moving Least-Squares (MLS) scheme. More >
Open Access
ABSTRACT
Chein-Shan Liu1, Yung-Wei Chen2, Jiang-Ren Chang2
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 93-100, 2007, DOI:10.3970/icces.2007.003.093
Abstract A new collocation method is developed here to solve the elliptic boundary value problems with singularities. Specifically, we consider the Motz problem as a test of the performance of the new method, which is found accurate and effective. More >
Open Access
ABSTRACT
I.K. Lifanov1, Y.A. Melnikov2, A.S. Nenashev3
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 101-106, 2007, DOI:10.3970/icces.2007.003.101
Abstract Two different boundary integral equation method-based approaches are developed for computing potential fields generated by point sources in multiply-connected regions of irregular configuration. Numerical experiment is conducted to demonstrate the computational potential of the approaches. More >
Open Access
ABSTRACT
R. Vignjevic1, T. De Vuyst2, J.C. Campbell1
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 107-112, 2007, DOI:10.3970/icces.2007.003.107
Abstract An approach to the treatment of contact problems involving frictionless sliding and separation under large deformations in meshless methods is proposed. The method is specially suited for non-structured spatial discretisation. The contact conditions are imposed using a contact potential for particles in contact. Inter-penetration is checked as a part of the neighbourhood search. In the case of conventional SPH contact conditions are enforced on the boundary layer 2h thick while in the case of the normalized SPH contact conditions are enforced for the particles lying on the contact surface. The implementation of the penalty based contact algorithm for the central… More >
Open Access
ABSTRACT
Suely Oliveira2, Fang Yang2
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 113-120, 2007, DOI:10.3970/icces.2007.003.113
Abstract In this paper we describe and compare preconditioners for saddle-point systems obtained from meshfree discretizations, using the concepts of hierarchical (or H-)matrices. Previous work by the authors using this approach did not use H-matrix techniques throughout, as is done here. Comparison shows the method described here to be better than the author's previous method, an AMG method adapted to saddle point systems, and conventional iterative methods such as JOR. More >
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