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A simple analytical parameterization for the water vapor millimeter wave foreign continuum

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER 2003年第1-4期82卷 517-531页

作者： Ma, Q Tipping, RH Columbia Univ Dept Appl Phys NASA Goddard Inst Space Studies New York NY 10025 USA Univ Alabama Dept Phys & Astron Tuscaloosa AL 35487 USA

We present a theoretical calculation of the millimeter wave foreign continuum due to colliding pairs of H2O-N-2 molecules. The theory is formulated using the symmetrized spectral density which ensures that the principle of detailed balance is. satisfied. It is based on the lanczos algorithm, and the resulting tri-diagonal matrix is written in terms of continued fractions. The calculations are carried out in the coordinate representation in which the basis functions are delta functions whose arguments are the angular variables necessary to specify the molecular orientations. In this representation, the anisotropic interaction potential responsible for the continuum absorption is diagonal, and the ensemble averages over the states become. multidimensional integrations. These are computed using the Monte Carlo method. The results, computed for a range of temperatures relevant to the atmosphere, are compared to laboratory measurements and to widely used empirical models. For easy use, we fit our results for the absorption coefficient to a simple analytic function of frequency and temperature. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： millimeter wave absorption water vapor lanczos algorithm

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A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2003年第41-42期192卷 4609-4640页

作者： Wagner, MM Pinsky, PM Oberai, AA Malhotra, M Stanford Univ Div Mech & Computat Stanford CA 94305 USA Boston Univ Dept Aerosp & Mech Engn Boston MA 02215 USA Sun Microsyst Inc Palo Alto CA USA

A Krylov subspace projection method which provides simultaneous solutions of the Helmholtz equation at multiple frequencies in one solution step is presented. The projector is obtained with an unsymmetric block lanczos algorithm applied to a transfer function derived from a finite element discretization. This approach is equivalent to a matrix valued Pade approximation of the transfer function. The proposed method is an extension of the formulation presented in [J. Comput. Acoust. 8 (2000) 223] to unsymmetric systems and allows the treatment of a much wider range of practical problems, including near-field and fluid-structure interaction computations. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multiple-frequency solution Krylov subspace lanczos algorithm Pade approximation Helmholtz equation Dirichlet-to-Neumann map acoustics

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Convergence of restarted Krylov subspaces to invariant subspaces

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2003年第4期25卷 1074-1109页

作者： Beattie, C Embree, M Rossi, J Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA Univ Oxford Comp Lab Oxford OX1 3QD England

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of nonnormality. Associated with a desired set of eigenvalues is a maximum "reachable invariant subspace" that can be developed from the given starting vector. Convergence for this distinguished subspace is bounded in terms involving a polynomial approximation problem. Elementary results from potential theory lead to convergence rate estimates and suggest restarting strategies based on optimal approximation points (e.g., Leja or Chebyshev points);exact shifts are evaluated within this framework. Computational examples illustrate the utility of these results. Origins of superlinear effects are also described.

关键词： Krylov subspace methods Arnoldi algorithm lanczos algorithm polynomial restarts invariant subspaces eigenvalues pseudospectra perturbation theory potential theory Zolotarev-type polynomial approximation problems

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Using Lebedev grids, sine spherical harmonics, and monomer contracted basis functions to calculate bending energy levels of HF trimer

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JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2003年第4期2卷 599-608页

作者： Wang, XG Carrington, T Univ Montreal Dept Chim Montreal PQ H3C 3J7 Canada

We calculate energy levels of a six-dimensional bending Hamiltonian for HF trimer using a finite basis representation (FBR) in conjunction with the lanczos eigensolver. We improve on our previous method [J. Chem. Phys. 115, 9781 (2001) using three techniques: (1) Lebedev's quadrature scheme is used to reduce the size of quadrature grid by a factor of 3.4. (2) Since the barrier separating the two equivalent versions of HF trimer is high and wide, it is a good approximation to confine the bending motion to one well by using sine spherical harmonics basis functions (this reduces the size of the basis by a factor of 8). (3) The sine spherical harmonic basis is contracted for each monomer to generate a very efficient basis. It is shown that the best approach is to combine all the three techniques.

关键词： HF trimer Lebedev grid contracted basis lanczos algorithm

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Krylov-subspace-based order reduction methods applied to generate compact-electro-thermal models for MEMS

Krylov-subspace-based order reduction methods applied to gen...

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Nanotechnology Conference and Trade Show (Nanotech 2003)

作者： Bechtold, T Salimbahrami, B Rudnyi, EB Lohmann, B Korvink, JG Univ Freiburg IMTEK D-79110 Freiburg Germany

ISBN: (纸本)0972842217

The high power dissipation density in today s miniature electronic/mechanical systems makes on-chip thermal management crucial. In order to achieve quick-to-evaluate, yet accurate electro-thermal models, needed for the thermal management of microsystems, model order reduction is necessary. In this paper, we use Krylov-subspace methods for the order reduction of a electro-thermal MEMS model, illustrated by a novel type of micropropulsion device. Comparison between different moment-matching algorithms including a new two-sided Arnoldi algorithm, is performed.

关键词： compact thermo-electric model order reduction. Krylov-subspace Arnoldi process lanczos algorithm

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Generalized eigenvalue problems: lanczos algorithm with a recursive partitioning method

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2000年第7-8期39卷 211-224页

作者： Sundar, S Bhagavan, BK Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

In this paper, the computation of the smallest eigenvalues and the corresponding eigenvectors of the generalized eigenvalue problem using lanczos algorithm with a recursive partitioning method as well as the Sturm sequence-bisection method have been discussed. We have also presented the comparison of the numerical results and the CPU-time between the above two methodologies. Our comparative study indicates that the lanczos with a recursive partitioning method takes relatively less computing time than that of the Sturm sequence-bisection method. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： Krylov subspace lanczos algorithm bisection method recursive partitioning algorithm generalized eigenvalue problem

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

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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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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 generating discrete orthogonal bivariate polynomials

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BIT NUMERICAL MATHEMATICS 2002年第2期42卷 393-407页

作者： Huhtanen, M Larsen, RM Stanford Univ Dept Comp Sci SCCM Program Stanford CA 94305 USA Stanford Univ WW Hansen Expt Phys Lab SOI MDI Stanford CA 94305 USA

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S subset of R-2. For this purpose we employ commuting pairs of real symmetric matrices H, K is an element of R-n x n to obtain, in a certain sense, a two dimensional Hermitian lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.

关键词： lanczos algorithm bivariate polynomial slowly growing length of the recurrence curve fitting least squares approximation bivariate interpolation

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CALCULATION OF TRANSITION AMPLITUDES WITH A SINGLE lanczos PROPAGATION

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Journal of Computational Biophysics and Chemistry 2002年第1期1卷 173-185页

作者： HUA GUO RONGQING CHEN DAIQIAN XIE Department of Chemistry University of New Mexico Albuquerque New Mexico 87131 USA Department of Chemistry and Institute of Theoretical and Computational Chemistry Nanjing University Nanjing Jiangsu 210093 P. R. China

We review in this article a recently proposed energy-global method that is capable of calculating the entire transition amplitude matrix with a single lanczos propagation. This method requires neither explicit computation nor storage of the eigenfunctions, rendering it extremely memory efficient. Procedures are proposed to handle situations where "spurious" eigenvalues aggregate around true eigenvalues due to round-off errors. This method is amenable to both real-symmetric and complex-symmetric Hamiltonians. Applications to molecular spectra and reactive scattering are presented. Its relationships with other methods are also discussed.

关键词： Transition amplitudes lanczos algorithm molecular spectroscopy reaction dynamics

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