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Haiyan Tian¹, Sergiy Reustkiy², C.S. Chen¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 169-176, 2007, DOI:10.3970/icces.2007.003.169
Abstract We introduce a new type of basis functions in this paper to approximate a scattered data set. We test our basis functions on recovering the well-known Franke's function given by scattered data. We then use these basis functions in Kansa's method for solving Helmholtz equations. To demonstrate our proposed approach, we compare the numerical solutions with analytic solutions. The numerical results show that our approach is accurate and efficient. More >

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W. Chen¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 177-188, 2007, DOI:10.3970/icces.2007.003.177
Abstract This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BKM employs the multiple reciprocity technique. Unlike the method of fundamental solution, the two methods use the non-singular general solution instead of the singular fundamental solution to circumvent the controversial artificial boundary outside the physical domain. Compared with the boundary element method, both BKM and BPM are meshfree, super-convergent, integration-free, symmetric, and mathematically simple collocation techniques for general PDEs. In particular, the BPM does not… More >

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687

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J. Bernal¹, S. Kanaun², V. Romero¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 189-194, 2007, DOI:10.3970/icces.2007.003.189
Abstract A new numerical method for the solution of integral equations of the theory of elasticity for bodies with cracks is developed. The method is based on a class of Gaussian approximating functions that simplify essentially the construction of the final matrix of the linear algebraic system of the discretized problem. The results of the application of the method to some plane problems of elasticity were compared with the exact solutions and some other numerical solutions that exist in literature. More >

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F. Cosmi¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 195-210, 2007, DOI:10.3970/icces.2007.003.195
Abstract The Cell Method is a recently developed numerical method that is giving interesting results in several fields of physics and engineering. In this paper, first a brief description of the method for elasticity problems is given and successively the elastodynamics formulation is derived. The method leads to an explicit solution system, combining the advantages of a diagonal mass matrix and the possibility of using unstructured meshes. The convergence rate has been tested in reference to the problem of free harmonic vibrations in a system with one degree of freedom, showing that the Cell Method has the same convergence rate of… More >

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806

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R.E. Meyers¹, K.S. Deacon¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 211-216, 2007, DOI:10.3970/icces.2007.003.211
Abstract Using a CCD camera we investigated and successfully achieved quantum ghost imaging of the stencil letters "ARL" placed in front of a photon bucket detector from photons which did not interact with the stencil letter object. We investigated the role of speckle spatial size and time scales in resolving images. The process suggests new mathematical paradigms and important applications for quantum ghost imaging . More >

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952

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S. Tanaka¹, H. Okada¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 217-224, 2007, DOI:10.3970/icces.2007.003.217
Abstract It has been recognized that the bottle-neck in solid/structural analyses using the finite element method is in their model generation phase. Methodologies that eliminate the needs for "elements" have been proposed by many researchers. They can be categorized into "meshless" and "virtually meshless" finite element methods. The "meshless" method may be represented by moving least square Ptrov-Galerkin (MLPG) method [1] and element free Galerkin Method (EFGM) [2]. The free-mesh method [3] and voxel finite element method [4], etc. are classified to be the "virtually meshless" approaches. The "meshless" methods eliminated needs for element connectivity information in their input data and… More >

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648

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Hans Mühlhaus¹, Laurent Bourgouin¹, Alina Hale¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 225-232, 2007, DOI:10.3970/icces.2007.003.225
Abstract We use a finite element formulation of the level set method to model the evolution of the free surface of axi-symmetric spreading flows of highly viscous media on a horizontal plane. We consider specifically the growth of a lava dome as an example however similar problems also occur in flows involving the spreading of molten metals or ceramics. Here we restrict ourselves on constant viscosity fluids for simplicity. In real lavas or melts the viscosity is highly temperature dependent. This manifests itself in the formation of thin predominantly elastic-plastic boundary layers along the free (cold) surfaces of the spreading flows.… More >

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660

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V. Romero¹, S. Kanaun²
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 233-242, 2007, DOI:10.3970/icces.2007.003.233
Abstract In this work Gaussian approximating functions proposed in the works of V. Maz'ya are used for the solution of the integral equations of elasto-plasticity for isotropic bodies. The use of this functions esentially simplify the calculation of the elements of the final matrix of the linear algebraic equations of the discretized problem. The elements of this matrix turn to be a combination of simple elementary functions. The method is applied to a 2D rectangular body that has a cut on a border and is subjected to axial tension. The convergence of the method is studied on this example. More >

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762

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Ye.Ye. Deryugin¹, G.V. Lasko^2,1, S. Schmauder²
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 243-250, 2007, DOI:10.3970/icces.2007.003.243
Abstract The results of 2D simulation of strain localizations on the meso-level in the surface layer of a polycrystal with a highly pronounced Portevin Le Chatelier (PLC) effect are presented. For such a purpose the Relaxation Element Method (REM) has been used. A fundamental property of solid "plastic deformation is accompanied by stress relaxation in local volumes of a loaded solid" lies on the basis of this method. The elaborated REM model operates on the principle of cellular automata. The results are in good qualitative agreement with known experimental data. More >

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696

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Zhenquan Li¹
The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 251-256, 2007, DOI:10.3970/icces.2007.003.251
Abstract An adaptive three-dimensional mesh refinement method based on the law of mass conservation has been introduced and tested using some analytical velocity fields as accurate in identifying singular point, asymptotic plane and drawing closed streamlines. This paper further investigates the adaptive mesh refinement method using a velocity field that is due to a uniform strain and a point vortex. Similar results have been obtained. More >

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