CMES-Vol. 16, No. 2, 2006

Open Access

ARTICLE

Distributed Finite Element Normalized Approximate Inverse Preconditioning
G.A. Gravvanis¹, K.M. Giannoutakis¹
CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 69-82, 2006, DOI:10.3970/cmes.2006.016.069
Abstract A new class of normalized explicit optimized approximate inverse finite element matrix techniques, based on normalized finite element approximate factorization procedures, for solving sparse linear systems resulting from the finite element discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse finite element matrix techniques for solving efficiently sparse finite element linear systems on distributed memory systems is also presented along with theoretical estimates on speedups and efficiency. The performance on a distributed memory machine, using Message Passing More >

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ARTICLE

3D Multi-Material Structural Topology Optimization with the Generalized Cahn-Hilliard Equations
Shiwei Zhou¹, Michael Yu Wang²
CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 83-102, 2006, DOI:10.3970/cmes.2006.016.083
Abstract This paper describes a self-mass-conservative Cahn-Hilliard (C-H) model with elastic strain energy (mean compliance) for the optimization of multi-material structure topology. The total free energy of the generalized C-H system can be represented as a Lyapunov functional so that the elastic strain energy, as a part of the total free energy, decreases gradually to attain optimal material distribution. The interface energy relating to phase gradient in the total free energy plays an important role in regularizing the original ill-posed problem by restricting the structure's boundaries. On the other hand, interface coalescence and break-up due to More >

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Investigations on the Accuracy and Condition Number for the Method of Fundamental Solutions
C.C. Tsai¹, Y.C. Lin², D.L. Young^2,3, S.N. Atluri⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 103-114, 2006, DOI:10.3970/cmes.2006.016.103
Abstract In the applications of the method of fundamental solutions, locations of sources are treated either as variables or a priori known constants. In which, the former results in a nonlinear optimization problem and the other has to face the problem of locating sources. Theoretically, farther sources results in worse conditioning and better accuracy. In this paper, a practical procedure is provided to locate the sources for various time-independent operators, including Laplacian, Helmholtz operator, modified Helmholtz operator, and biharmonic operator. Wherein, the procedure is developed through systematic numerical experiments for relations among the accuracy, condition number, and More >

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A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis
Timon Rabczuk¹, Pedro Areias²
CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 115-130, 2006, DOI:10.3970/cmes.2006.016.115
Abstract This paper proposes a meshfree method for arbitrary evolving cracks in thin shells. The approach is an improvement of the method proposed by Rabczuk T., Areias P.M.A., Belytschko T. (A meshfree thin shell for large deformation, finite strain and arbitrary evolving cracks, International Journal for Numerical Methods in Engineering). In the above cited paper, a shell was developed based on an intrinsic basis of third order completeness. Third order completeness was necessary to remove membrane locking. This resulted in the use of very large domains of influence that made the method computationally expensive. If the More >

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ARTICLE

A Fast Space-Time BEM Method for 3D Elastodynamics
J. X. Zhou¹, T. Koziara¹, T. G. Davies¹
CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 131-140, 2006, DOI:10.3970/cmes.2006.016.131
Abstract The classical BEM approach for elastodynamics can produce poor results when high gradients are generated by impulses. High gradient areas evolve over time and their locations are unknown a priori, so they usually can not be captured by uniform meshes. In this paper, we propose a novel method which interpolates both spatial and temporal domains. A direct space-time discretization scheme is used to capture the wave fronts accurately and to forestall generation of spurious oscillations there. Some numerical examples are given to demonstrate the power and scope of the method. More >

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