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 >

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 >

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 >

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 >

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 >

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 >

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 >

A. Tadeu¹, L. Godinho¹, J. António¹, P. Amado Mendes¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.3, pp. 163-168, 2007, DOI:10.3970/icces.2007.003.163

Abstract This paper evaluates the 3D wave propagation in an elastic slab containing cracks whose geometry does not change along the direction parallel to the formation surfaces. Two different formulations are used and compared: the Traction Boundary Element Method (TBEM) and the Method of Fundamental Solutions (MFS). Both approaches are developed in the frequency domain and surmount the thin-body difficulty posed by the classical Boundary Element Method (BEM). The TBEM models the crack as a single line. The resulting hypersingular integrals are evaluated analytically. For the MFS, the solution is approximated in terms of a linear combination of fundamental solutions, generated… More >

J. António¹ , A. Tadeu¹, L. Godinho

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.3, pp. 157-162, 2007, DOI:10.3970/icces.2007.003.157

Abstract A frequency dependent formulation based on the Method of Fundamental Solutions (MFS) is used to simulate the sound wave propagation in a 3D acoustic space. This solution is approximated by a linear combination of fundamental solutions generated by virtual sources placed outside the domain in order to avoid singularities. The coating materials can be assumed to be absorbent. This is achieved in the model prescribing the impedance that is defined as a function of the absorption coefficient. The model is first verified against analytical solutions, provided by the image source technique for a parallelepiped room bounded by rigid walls. The… More >

M.D. de Tullio¹, P. De Palma¹, G. Pascazio¹, M. Napolitano¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.3, pp. 151-156, 2007, DOI:10.3970/icces.2007.003.151

Abstract This paper provides a numerical method based on the immersed boundary approach for computing compressible viscous flows. The efficency of the method is enhanced by using a flexible local grid refinement technique which is obtained by coarsening a uniformly fine mesh far from high-gradient flow regions, such as boundary layers and shocks. More >