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Robust finite-element solution of lossy and unbounded Lelectromagnetic eigenvalue problems

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2002年第10期50卷 2331-2338页

作者： Zhu, Y Cangellaris, AC Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

An efficient algorithm is presented for the finite-element solution of electromagnetic eigenvalue problems associated with lossy and unbounded structures. The algorithm is based on the (E) over right arrow - (B) over right arrow formulation of the finite-element approximation of the electromagnetic equations. The special relationship between the vector bases used for the expansion of the electric field vector (E) over right arrow and the magnetic flux density vector (B) over right arrow is used to reduce the computational complexity of the proposed formulation. The occurrence of spurious de modes is avoided through the careful selection of divergence-free initial vectors in the Lanezos-Arnoldi-based iterative schemes used by the proposed algorithm. The resultant algorithm is only marginally more expensive than standard finite-element-based algorithms used for electromagnetic eigenvalue problems involving lossless structures. Numerical experiments from the application of the proposed algorithm to the eigenvalue analysis of both lossless and lossy cavities are used to demonstrate its accuracy, computational efficiency, and robustness.

关键词： Arnoldi algorithm eigenvalue problems finite-element method lanczos algorithm lossy media unbounded media

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Modes and modal analysis of three-dimensional (3D) structures based on the smoothed finite element methods (S-FEMs) using automatically generatable tetrahedral meshes

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2022年 140卷 262-281页

作者： Zhao, J. G. Liu, G. R. Huo, S. H. Li, Z. R. [a]School of Mechanical Engineering Hebei University of Technology Tianjin 300401 China [b]National Engineering Research Center for Technological Innovation Method and Tool Hebei University of Technology Tianjin 300401 China [c]Department of Aerospace Engineering and Engineering Mechanics University of Cincinnati OH 45221 USA

The smoothed finite element methods (S-FEMs) have been found capable of producing softer models whose "stiffness" is closer to the true continuous model. This paper explores, for the first time, this unique feature of SFEMs to develop a complete formulism and procedure to study free vibration and forced vibration of solid structures, via (1) solving eigenvalue problems that produces vibration modes of a given structure;(2) using model superimposition techniques and the lanczos algorithm to obtain transient dynamic solution for structures subjected to arbitrary dynamics forces. The present S-FEM modeling takes the advantageous of the so-called softening effects achieved by establishing proper types of smoothing domains based on edges and faces of the mesh known as ES/FS-FEM, so as to obtain accurate modes for both free and forced vibration analysis. For easy automation in creating 3D solids, we use only the automatically generatable tetrahedral mesh, while to ensure excellent stress solution using the ES/FS-FEM models. A 3D code has been developed in the framework of SFEMs, and applied to solve a number of 3D solid structures. The results are compared with those from the commercial finite element analysis software ABAQUS in terms of accuracy and convergence.

关键词： Smoothed finite element method Free vibration Forced vibration lanczos algorithm Mode superposition method ABAQUS

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Quadrature rule-based bounds for functions of adjacency matrices

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LINEAR ALGEBRA AND ITS APPLICATIONS 2010年第3期433卷 637-652页

作者： Benzi, Michele Boito, Paola Emory Univ Dept Math & Comp Sci Atlanta GA 30322 USA

Bounds for entries of matrix functions based on Gauss-type quadrature rules are applied to adjacency matrices associated with graphs. This technique allows to develop inexpensive and accurate upper and lower bounds for certain quantities (Estrada index, subgraph centrality, communicability) that describe properties of networks. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Graphs Networks Estrada index Subgraph centrality Communicability Sparse matrices Quadrature rules lanczos algorithm Decay bounds Matrix exponential Resolvent

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Removal of spurious DC modes in edge element solutions for modeling three-dimensional resonators

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2006年第7期54卷 3019-3025页

作者： Venkatarayalu, Neelakantam V. Lee, Jin-Fa Natl Univ Singapore Temasek Labs Singapore 117508 Singapore Natl Univ Singapore Dept Elect & Comp Engn Singapore 117508 Singapore Ohio State Univ Dept Elect & Comp Engn ElectroSci Lab Columbus OH 43210 USA

When using edge element basis functions for the solution of eigenmodes of the vector wave equation, "dc spurious modes" are introduced. The eigenvalues of these modes are zero and their corresponding eigenvectors are in the null space of the curl operator. These modes arise due to the irrotational vector space spanned by the edge element basis functions and lead to nonzero divergence of the electric flux. We introduce a novel method to eliminate the occurrence of such solutions using "divergence-free" constraint equations. The constraint equations are imposed efficiently by tree-cotree partitioning of the finite-element mesh and does not require any basis functions other than the edge elements. The constraint equations can be directly incorporated into any Krylov-subspace-based eigenvalue solver, such as the Lanezos/Arnoldi algorithm used widely for the solution of generalized sparse eigenvalue problems.

关键词： constraint equations finite-element method (FEM) lanczos algorithm spurious modes

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Nuclear spin-lattice relaxation at field-induced level crossings in a Cr₈F₈ pivalate single crystal

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PHYSICA B-CONDENSED MATTER 2016年 481卷 224-231页

作者： Yamamoto, Shoji Hokkaido Univ Dept Phys Sapporo Hokkaido 0600810 Japan

We construct a microscopic theory for the proton spin-lattice relaxation-rate 1/T-1 measurements around field-induced level crossings in a single crystal of the trivalent chromium ion wheel complex [Cr8F8(OOCtBu)(16)] at sufficiently low temperatures [E. Micotti et al., Phys. Rev. B 72 (2005) 020405(R)]. Exactly diagonalizing a well-equipped spin Hamiltonian for the individual clusters and giving further consideration to their possible interactions, we reveal the mechanism of 1/T-1] being single-peaked normally at the first level crossing but double-peaked intriguingly around the second level crossing. We wipe out the doubt about poor crystallization and find out a solution intramolecular alternating Dzyaloshinsky-Moriya interaction combined with intermolecular coupling of antiferromagnetic character, each of which is so weak as several tens of mK in magnitude. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Molecular ring antiferromagnet Field-induced level crossing Nuclear spin-lattice relaxation Recursion method lanczos algorithm

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Full-wave analysis of multiconductor transmission lines on anisotropic inhomogeneous substrates

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1999年第9期47卷 1764-1770页

作者： Radhakrishnan, K Chew, WC Univ Illinois Dept Elect & Comp Engn Ctr Computat Electromagnet Urbana IL 61801 USA

The full-wave analysis of the generalized microstrip line on an inhomogeneous anisotropic substrate is carried out by using the finite-difference method. The resulting sparse matrix equation is solved efficiently using the bi-lanczos algorithm, The use of the inhomogeneous wave equation to formulate the problem makes it easy to analyze structures with multilayered substrates, The algorithm can analyze complicated structures with multiple conductors at arbitrary locations. A spatial interpolation scheme is used to evaluate the contribution from the off-diagonal terms in <(mu)over bar> and <(epsilon)over bar> The use of the bi-lanczos algorithm allows us to solve the problem at O(N-1.5) complexity. Storage requirements can be made to scale as O(N), This makes it possible to analyze large problems on a small computer. Very good agreement is seen between published results and results obtained using this technique.

关键词： anisotropic substrate finite difference lanczos algorithm microstrip lines

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Parallel computation of pseudospectra of large sparse matrices

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PARALLEL COMPUTING 2002年第2期28卷 199-221页

作者： Mezher, D Philippe, B Inst Natl Rech Informat & Automat IRISA F-35042 Rennes France USJ ESIB Beirut Lebanon

The parallel computation of the pseudospectrum is presented. The Parallel Path following algorithm using Triangles (PPAT) is based on the Path following algorithm using Triangles (PAT). This algorithm offers total reliability and can handle singular points along the level curve without difficulty. Furthermore, PPAT offers a guarantee of termination even in the presence of round-off errors and makes use of the large granularity for parallelism in PAT. This results in large speedups and high efficiency. The PPAT is able to trace multiple level curves simultaneously and takes into account the symmetry of the pseudospectrum in the case of real matrices to reduce the total computational cost. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： pseudospectrum lanczos algorithm multifrontal QR decomposition parallelism

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ON EFFICIENT NUMERICAL APPROXIMATION OF THE BILINEAR FORM c* A^-1b

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2011年第2期33卷 565-587页

作者： Strakos, Zdenek Tichy, Petr Charles Univ Prague Fac Math & Phys Prague 18675 Czech Republic Acad Sci Czech Republic Inst Comp Sci Prague 18207 Czech Republic

Let A is an element of C-NxN be a nonsingular complex matrix and b and c be complex vectors of length N. The goal of this paper is to investigate approaches for efficient approximations of the bilinear form c* A(-1)b. Equivalently, we wish to approximate the scalar value c* x, where x solves the linear system Ax = b. Here the matrix A can be very large or its elements can be too costly to compute so that A is not explicitly available and it is used only in the form of the matrix-vector product. Therefore a direct method is not an option. For A Hermitian positive definite, b* A(-1)b can be efficiently approximated as a by-product of the conjugate-gradient iterations, which is mathematically equivalent to the matching moment approximations computed via the Gauss-Christoffel quadrature. In this paper we propose a new method using the biconjugate gradient iterations which is applicable to the general complex case. The proposed approach will be compared with existing ones using analytic arguments and numerical experiments.

关键词： bilinear forms scattering amplitude method of moments Krylov subspace methods conjugate gradient method biconjugate gradient method lanczos algorithm Arnoldi algorithm Gauss-Christoffel quadrature model reduction

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On the computation of few eigenvalues of positive definite Hamiltonian matrices

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FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2006年第4期22卷 403-411页

作者： Amodio, P Univ Bari Dipartimento Matemat I-70125 Bari Italy

Given a Hamiltonian matrix H = JS with S symmetric and positive definite, we analyze a symplectic lanczos algorithm to transform -H-2 in a symmetric and positive definite tridiagonal matrix of half size. By means of two effective restarted procedures, this algorithm is then used to compute few extreme eigenvalues of H. Numerical examples are also reported to compare the presented techniques. (c) 2004 Elsevier B.V. All rights reserved.

关键词： Hamiltonian matrices eigenvalues lanczos algorithm

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Out-of-core SVD performance for document indexing

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APPLIED NUMERICAL MATHEMATICS 2007年第11-12期57卷 1230-1239页

作者： Martin, Dian I. Martin, John C. Berry, Michael W. Browne, Murray Univ Tennessee Dept Comp Sci Knoxville TN 37996 USA Small Bear Tech Consulting Thorn Hill TN 37881 USA

The following study documents a formal evaluation of the performance tradeoffs and scalability for computing the sparse matrix singular value decomposition (SVD) as part of the Latent Semantic Analysis (LSA) of a given document collection with an out-of-core process. Most software packages capable of computing the SVD do all of their processing in-core, which involves keeping all vectors for the computation in memory. This limits the size of document collections that can be processed. The goal of the study was specifically to evaluate software capable of performing the SVD calculations out-of-core, minimizing memory usage by keeping only a small set of work vectors in memory at a time. Performance measures of interest for this study included the time of execution, both in CPU time and wall clock time, as well the memory and disk usage for computing the SVD. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： lanczos algorithm latent semantic analysis out-of-core singular value decomposition

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