Liviu Marin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 99-122, 2008, DOI:10.3970/cmes.2008.030.099

Abstract The application of the method of fundamental solutions (MFS) to inverse boundary value problems associated with the steady-state heat conduction in isotropic media in the presence of sources, i.e. the Poisson equation, is investigated in this paper. Based on the approach of Alves and Chen (2005), these problems are solved in two steps, namely by finding first an approximate particular solution of the Poisson equation and then the numerical solution of the resulting inverse boundary value problem for the Laplace equation. The resulting MFS discretised system of equations is ill-conditioned and hence it is solved More >

Sanjay Mittal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 63-78, 2008, DOI:10.3970/cmes.2008.027.063

Abstract Flow past a circular cylinder looses stability at a Reynolds number,Re~47. It has been shown, in the past, that the linear stability analysis (LSA) of the steady state solution can predict not only the critical Re, but also the non-dimensional frequency, St, of the associated instability. For larger Re the non-linear effects become important and the LSA of the steady-state flow does not predict the correct St. It is shown that, in general, the LSA applied to the time-averaged flow can result in useful information regarding its stability. This idea is applied to the Re = 100 flow past More >

Arezoo Emdadi¹, Edward J. Kansa², Nicolas Ali Libre^1,3, Mohammad Rahimian¹, Mohammad Shekarchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.1, pp. 23-42, 2008, DOI:10.3970/cmes.2008.025.023

Abstract We present a new method based upon the paper of Volokh and Vilney (2000) that produces highly accurate and stable solutions to very ill-conditioned multiquadric (MQ) radial basis function (RBF) asymmetric collocation methods for partial differential equations (PDEs). We demonstrate that the modified Volokh-Vilney algorithm that we name the improved truncated singular value decomposition (IT-SVD) produces highly accurate and stable numerical solutions for large values of a constant MQ shape parameter, c, that exceeds the critical value of c based upon Gaussian elimination. More >

Nicolas Ali Libre^1,2, Arezoo Emdadi², Edward J. Kansa^3,4, Mohammad Rahimian², Mohammad Shekarchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.1, pp. 61-80, 2008, DOI:10.3970/cmes.2008.024.061

Abstract The numerical solution of partial differential equations (PDEs) with Neumann boundary conditions (BCs) resulted from strong form collocation scheme are typically much poorer in accuracy compared to those with pure Dirichlet BCs. In this paper, we show numerically that the reason of the reduced accuracy is that Neumann BC requires the approximation of the spatial derivatives at Neumann boundaries which are significantly less accurate than approximation of main function. Therefore, we utilize boundary treatment schemes that based upon increasing the accuracy of spatial derivatives at boundaries. Increased accuracy of the spatial derivative approximation can be… More >

Z. D. Han, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 41-52, 2007, DOI:10.3970/cmes.2007.021.041

Abstract Straight-forward systematic derivations of the weakly singular boundary integral equations (BIEs) are presented, following the simple and directly-derived approach by Okada, Rajiyah, and Atluri (1989b) and Han and Atluri (2002). A set of weak-forms and their algebraic combinations have been used to avoid the hyper-singularities, by directly applying the "intrinsic properties'' of the fundamental solutions. The systematic decomposition of the kernel functions of BIEs is presented for regularizing the BIEs. The present approach is general, and is applied to developing weakly-singular BIEs for solids and acoustics successfully. More >

R. Vodička¹, V. Mantič², F. París²

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 173-204, 2007, DOI:10.3970/cmes.2007.017.173

Abstract An original approach to solve domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach, based on a new variational principle for such problems, yields a fully symmetric system of equations. A natural property of the proposed approach is its capability to deal with nonconforming discretizations along straight and curved interfaces, allowing in this way an independent meshing of non-overlapping subdomains to be performed. Weak coupling conditions of equilibrium and compatibility at an interface are obtained from the critical point conditions of the energy functional. Equilibrium is imposed through local traction… More >

L. Godinho A. ¹, A. Tadeu¹, P. Amado Mendes¹

CMC-Computers, Materials & Continua, Vol.5, No.2, pp. 117-128, 2007, DOI:10.3970/cmc.2007.005.117

Abstract This paper presents a strategy for using the Method of Fundamental Solutions (MFS) to model the propagation of elastic waves around thin structures, like empty cracks or thin rigid screens, located in a homogeneous elastic medium. The authors make use of a simple approach for modeling these propagation conditions using the MFS together with decomposition of the domain into distinct regions. This approach makes it possible to avoid the undetermined system of equations that arises from imposing boundary conditions at both sides of a thin structure. The numerical implementation of the MFS is performed in… More >

MARCOS S. DREON¹, HORACIO HERAS^1,2, RICARDO J. POLLERO¹

BIOCELL, Vol.30, Suppl.S, pp. 359-365, 2006

Abstract This article has no abstract. More >

Taeyoung Ha¹, Sangwon Seo², Dongwoo Sheen³

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.1, pp. 57-76, 2006, DOI:10.3970/cmes.2006.014.057

Abstract We present nonoverlapping domain decomposition methods for the approximation of both electromagnetic fields in a three-dimensional bounded domain satisfying absorbing boundary conditions. A Seidel-type domain decomposition iterative method is introduced based on a hybridization of a nonconforming mixed finite element method. Convergence results for the numerical procedure are proved by introducing a suitable pseudo-energy. The spectral radius of the iterative procedure is estimated and a method for choosing an optimal matching parameter is given. A red-black Seidel-type method which is readily parallelizable is also introduced and analyzed. Numerical experiments confirm that the presented algorithms are faster than More >

C.W. Chen¹, C.M. Fan¹, D.L. Young^1,2, K. Murugesan¹, C.C Tsai³

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.1, pp. 29-44, 2005, DOI:10.3970/cmes.2005.008.029

Abstract We use a meshless numerical method to analyze the eigenanalysis of thin circular membranes with degenerate boundary conditions, composed by different orientations and structures of stringers. The membrane eigenproblem is studied by solving the two-dimensional Helmholtz equation utilizing the method of fundamental solutions and domain decomposition technique as well. The method of singular value decomposition is adopted to obtain eigenvalues and eigenvectors of the resulting system of global linear equation. The proposed novel numerical scheme was first validated by three circular membranes which are structured with a single edge stringer, two opposite edge stringers and… More >