CMES-Vol. 60, No. 3, 2010

Open Access

ARTICLE

Unconditionally Stable Convergence with Power Principle-based Time-Integration Schemes
G. Formica¹, F. Milicchio²
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 199-220, 2010, DOI:10.3970/cmes.2010.060.199
Abstract This manuscript introduces a novel sufficient condition for the unconditionally stable convergence of the general class of trapezoidal integrators. Contrary to standard energy-based approaches, this convergence criterion is derived from the power principles, in terms of both balance and dissipation. This result improves the well-known condition of stable convergence based on the energy method, extending its applicative spectrum to a variety of physical problems, whose constitutive prescriptions may be more appropriately characterized by means of evolving field equations. Our treatment, tailored for generalized trapezoidal integrators, addresses both linear and nonlinear problems, extending its applicability to More >

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Reconstruction of Boundary Data in Two-Dimensional Isotropic Linear Elasticity from Cauchy Data Using an Iterative MFS Algorithm
Liviu Marin¹
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 221-246, 2010, DOI:10.3970/cmes.2010.060.221
Abstract We investigate the implementation of the method of fundamental solutions (MFS), in an iterative manner, for the algorithm of Kozlov, Maz'ya and Fomin (1991) in the case of the Cauchy problem in two-dimensional isotropic linear elasticity. At every iteration, two mixed well-posed and direct problems are solved using the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion is also presented. The iterative MFS algorithm is tested for Cauchy problems for isotropic linear elastic materials to confirm the numerical More >

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Efficient Cohomology Computation for Electromagnetic Modeling
Paweł Dłotko¹, Ruben Specogna²
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 247-278, 2010, DOI:10.3970/cmes.2010.060.247
Abstract The systematic potential design is of high importance in computational electromagnetics. For example, it is well known that when the efficient eddy-current formulations based on a magnetic scalar potential are employed in problems which involve conductive regions with holes, the so-calledthick cutsare needed to make the boundary value problem well defined. Therefore, a considerable effort has been invested over the past twenty-five years to develop fast and general algorithms to compute thick cuts automatically. Nevertheless, none of the approaches proposed in literature meet all the requirements of being automatic, computationally efficient and general. In this More >

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Novel Algorithms Based on the Conjugate Gradient Method for Inverting Ill-Conditioned Matrices, and a New Regularization Method to Solve Ill-Posed Linear Systems
Chein-Shan Liu¹, Hong-Ki Hong¹, Satya N. Atluri²
CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 279-308, 2010, DOI:10.3970/cmes.2010.060.279
Abstract We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting ill-conditioned matrices, we add a vector equation into the given matrix equation for obtaining the left-inversion of matrix (and a similar vector equation for the right-inversion) and thus we obtain an over-determined system. The resulting two modifications… More >

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