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Finite Element Matrices (finite + element_matrix)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Ritz finite elements for curvilinear particles

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2006
Paul R. Heyliger
Abstract A general finite element is presented for the representation of fields in curvilinear particles in two and three dimensions. The formulation of this element shares many similarities with usual finite element approximations, but differs in that nodal points are defined in part by contact points with other particles. Power series in the geometric coordinates are used as the starting basis functions, but are recast in terms of the field variables within the particle interior and the points of contact with other elements. There is no discretization error and the elements of the finite element matrices can all be evaluated in closed form. This approach is applicable to shapes in two and three dimensions, including discs, ellipses, spheres, spheroids, and potatoes. Examples are included for two-dimensional applications of steady-state heat transfer and elastostatics. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Sparse factorization of finite element matrices using overlapped localizing solution modes

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 4 2008
J.-S. Choi
Abstract Local-global solution (LOGOS) modes provide a computationally efficient framework for developing fast, direct solution methods for electromagnetic simulations. In this article, we demonstrate that the LOGOS framework yields fast direct solutions for finite element discretizations of the wave equation in two dimensions. For fixed-frequency applications, numerical examples demonstrate that the memory and CPU complexities of the proposed solver are nearly linear. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1050,1054, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23298 [source]

Two-level preconditioners for serendipity finite element matrices

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2006
Yuri R. Hakopian
Abstract In this paper an approach to construct algebraic multilevel preconditioners for serendipity finite element matrices is presented. Two-level preconditioners constructed in the paper allow to obtain multilevel preconditioners in serendipity case using multilevel preconditioners for linear finite element matrices. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Algebraic multilevel preconditioning of finite element matrices using local Schur complements

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2006
J. K. Kraus
Abstract We consider an algebraic multilevel preconditioning technique for SPD matrices arising from finite element discretization of elliptic PDEs. In particular, we address the case of non-M matrices. The method is based on element agglomeration and assumes access to the individual element matrices. The left upper block of the considered multiplicative two-level preconditioner is approximated using incomplete factorization techniques. The coarse-grid element matrices are simply Schur complements computed from local neighbourhood matrices, i.e. small collections of element matrices. Assembling these local Schur complements results in a global Schur complement approximation that can be analysed by regarding (local) macro elements. These components, when combined in the framework of an algebraic multilevel iteration, yield a robust and efficient linear solver. The presented numerical experiments include also the Lamé differential equation for the displacements in the two-dimensional plane-stress elasticity problem. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Algebraic multigrid Laplace solver for the extraction of capacitances of conductors in multi-layer dielectrics

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 5 2007
Prasad S. Sumant
Abstract This paper describes the development of a robust multigrid, finite element-based, Laplace solver for accurate capacitance extraction of conductors embedded in multi-layer dielectric domains. An algebraic multigrid based on element interpolation is adopted and streamlined for the development of the proposed solver. In particular, a new, node-based agglomeration scheme is proposed to speed up the process of agglomeration. Several attributes of this new method are investigated through the application of the Laplace solver to the calculation of the per-unit-length capacitance of configurations of parallel, uniform conductors embedded in multi-layer dielectric substrates. These two-dimensional configurations are commonly encountered as high-speed interconnect structures for integrated electronic circuits. The proposed method is shown to be particularly robust and accurate for structures with very thin dielectric layers characterized by large variation in their electric permittivities. More specifically, it is demonstrated that for such geometries the proposed node-based agglomeration systematically reduces the problem size and speeds up the iterative solution of the finite element matrix. Copyright © 2007 John Wiley & Sons, Ltd. [source]