CMES-Vol. 92, No. 1, 2013

Open Access

ARTICLE

Compact Local IRBF and Domain Decomposition Method for solving PDEs using a Distributed termination detection based parallel algorithm
N. Pham-Sy¹, C.-D. Tran¹, T.-T. Hoang-Trieu¹, N. Mai-Duy¹, T. Tran-Cong¹
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 1-31, 2013, DOI:10.3970/cmes.2013.092.001
Abstract Compact Local Integrated Radial Basis Function (CLIRBF) methods based on Cartesian grids can be effective numerical methods for solving partial differential equations (PDEs) for fluid flow problems. The combination of the domain decomposition method and function approximation using CLIRBF methods yields an effective coarse-grained parallel processing approach. This approach has enabled not only each sub-domain in the original analysis domain to be discretised by a separate CLIRBF network but also compact local stencils to be independently treated. The present algorithm, namely parallel CLIRBF, achieves higher throughput in solving large scale problems by, firstly, parallel processing More >

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An approximately H¹-optimal Petrov-Galerkin meshfree method: application to computation of scattered light for optical tomography
N Pimprikar¹, J Teresa², D Roy^1,3, R M Vasu⁴, K Rajan⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 33-61, 2013, DOI:10.3970/cmes.2013.092.033
Abstract Nearly pollution-free solutions of the Helmholtz equation for k-values corresponding to visible light are demonstrated and verified through experimentally measured forward scattered intensity from an optical fiber. Numerically accurate solutions are, in particular, obtained through a novel reformulation of the H1 optimal Petrov-Galerkin weak form of the Helmholtz equation. Specifically, within a globally smooth polynomial reproducing framework, the compact and smooth test functions are so designed that their normal derivatives are zero everywhere on the local boundaries of their compact supports. This circumvents the need for a priori knowledge of the true solution on the More >

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A new implementation of the numerical manifold method (NMM) for the modeling of non-collinear and intersecting cracks
Y.C. Cai^1,2,3, J. Wu², S.N. Atluri³
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 63-85, 2013, DOI:10.3970/cmes.2013.092.063
Abstract The numerical manifold method (NMM), based on the finite covers, unifies the continuum analyses and discontinuum analyses without changing a predefined mathematical mesh of the uncracked solid, and has the advantages of being concise in theory as well as being clear in concept. It provides a natural method to analyze complex shaped strong discontinuities as well as weak discontinuities such as multiple cracks, intersecting cracks, and branched cracks. However, the absence of an effective algorithm for cover generation, to date, is still a bottle neck in the research and application in the NMM. To address… More >

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Navier-Stokes model with viscous strength
K.Y. Volokh^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 87-101, 2013, DOI:10.3970/cmes.2013.092.087
Abstract In the laminar mode interactions among molecules generate friction between layers of water that slide with respect to each other. This friction triggers the shear stress, which is traditionally presumed to be linearly proportional to the velocity gradient. The proportionality coefficient characterizes the viscosity of water. Remarkably, the standard Navier-Stokes model surmises that materials never fail – the transition to turbulence can only be triggered by some kinematic instability of the flow. This premise is probably the reason why the Navier-Stokes theory fails to explain the so-called subcritical transition to turbulence with the help of… More >

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ARTICLE

A Regularized Method of Fundamental Solutions Without Desingularization
C. Gáspár¹
CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 103-121, 2013, DOI:10.3970/cmes.2013.092.103
Abstract Some regularized versions of the Method of Fundamental Solutions are investigated. The problem of singularity of the applied method is circumvented in various ways using truncated or modified fundamental solutions, or higher order fundamental solutions which are continuous at the origin. For pure Dirichlet problems, these techniques seem to be applicable without special additional tools. In the presence of Neumann boundary condition, however, they need some desingularization techniques to eliminate the appearing strong singularity. Using fundamental solutions concentrated to lines instead of points, the desingularization can be omitted. The method is illustrated via numerical examples. More >

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