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IEEE International Power Modulator and High Voltage Conference (IPMHVC)

作者： Jackson, Robert H. Verboncoeur, John P. Calabazas Creek Res Inc San Mateo CA 94404 USA Michigan State Univ Dept Elect Commun Engn E Lansing MI 48824 USA

ISBN: (纸本)9781467312257;9781467312226

The Local Taylor Polynomial (LTP) method treats fields and sources as local analytic polynomials for rapid numerical solution of PDE's. Knowledge of the source polynomial would allow sources to be treated analytically in LTP formulas, since the derivatives follow directly for polynomial forms. Aside from idealized cases, such information is seldom available;however, use of macro-particles with finite polynomial shape functions for charge and current deposition can make analytic treatment possible for general cases. The macro-particle polynomial coefficients can be used directly in LTP solution formulas. This scheme allows one to choose a representation of particles that enables high fidelity with fewer particles compared to traditional particle methods, since the polynomials can include information such as transverse profile information from a beam, for example. This paper presents a simple polynomial form for representing macro-particles in numerical simulations. The particle shape must be continuous and differentiable to a specified order, bounded in size and magnitude, zero in magnitude and derivatives at the edges, symmetric, positive definite, with analytic coefficients. Two key properties for use in LTP will be demonstrated: zero derivatives at the particle boundary and analytically computable coefficients.

关键词： numerical algorithm Space Charge Poisson Equation Particle-in-Cell Plasma Simulation

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numerical Study of Inverse Problems of Nonscattering Anisotropic Shell Theory

Numerical Study of Inverse Problems of Nonscattering Anisotr...

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2012 3rd International Conference on Applied Mechanics and Mechanical Engineering(ICAMME 2012)

作者： Alekseev Gennady Lobanov Aleksey Grenkin Gleb Far Eastern Federal University Institute of Applied Mathematics FEB RAS

The inverse problems are formulated for generalized Helmholtz equation describing propagation of acoustics waves in inhomogeneous anisotropic medium. These problems are connected with constructing nonscattering shells filled with anisotropic fluid. For solving the inverse problems we apply the nonlinear optimization techniques. Based on this approach we formulate the general control problem for the Helmholtz equation under consideration. The control problem consists of minimization of a suitable cost functional depending on the state(acoustic pressure) and unknown functions(controls). The optimality system for the general control problem is derived, the sufficient conditions for data which provide a local stability and uniqueness of control problems under study for concrete tracking-type cost functionals are discussed. The efficient numerical algorithm of solving control problem under study based on Newton's method of solving nonlinear equations and finite element for Helmholtz boundary value problems is proposed.

关键词： Acoustics anisotropic media inverse problems control problems optimality system numerical algorithm cloaking shells

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Optimization of a Simulated Well Cluster using Surrogate Models

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IFAC Proceedings Volumes 2012年第8期45卷 275-280页

作者： Bjarne Grimstad Håvard Ausen Victoria Lervik Vidar Gunnerud Dag Ljungquist Department for Engineering Cybernetics NTNU Department of Industrial Economics and Technology Management NTNU FMC Technologies Asker Norway

In this paper we present an implementation of a partly Derivative-Free Optimization (DFO) algorithm for production optimization of a simulated multi-phase flow network. The network consists of well and pipeline simulators, considered to be black-box models without available gradients. The algorithm utilizes local approximations as surrogate models for the complex simulators. A Mixed Integer Nonlinear Programming (MINLP) problem is built from the surrogate models and the known structure of the flow network. The core of the algorithm is IBM's MINLP solver Bonmin, which is run iteratively to solve optimization problems cast in terms of surrogate models. At each iteration the surrogate models are updated to fit local data points from the simulators. The algorithm is tested on an artificial subsea network modeled in FlowManager ™ , a multi-phase flow simulator from FMC Technologies. The results for this special case show that the algorithm converges to a point where the surrogate models fit the simulator, and they both share the optimum.

关键词： Derivative-Free Optimization Non-linear Optimization Non-convex Optimization Mixed Integer Programming Process Simulators Interpolation algorithm numerical algorithm

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numerical algorithm for the retrieval of spatial coherence properties of partially coherent beams from transverse intensity measurements

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OPTICS EXPRESS 2007年第21期15卷 13613-13623页

作者： Rydberg, Christer Bengtsson, Joergen Micron Laser Syst AB SE-18303 Taby Sweden Chalmers Univ Technol Photon Lab MC2 SE-41296 Gothenburg Sweden

A novel algorithm for the retrieval of the spatial mutual coherence function of the optical field of a light beam in the quasimonochromatic approximation is presented. The algorithm only requires that the intensity distribution is known in a finite number of transverse planes along the beam. The retrieval algorithm is based on the observation that a partially coherent field can be represented as an ensemble of coherent fields. Each field in the ensemble is propagated with coherent methods between neighboring planes, and the ensemble is then subjected to amplitude restrictions, much in the same way as in conventional phase recovery algorithms for coherent fields. The proposed algorithm is evaluated both for one- and two-dimensional fields using numerical simulations. (C) 2007 Optical Society of America.

关键词： .spatial coherence intensity distribution phase retrieval propagated numerical algorithm proposed algorithm retrieval algorithm quasimonochromatic transverse planes transverse intensity

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A differential algorithm for the Lyapunov spectrum

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PHYSICA D-NONLINEAR PHENOMENA 2011年第16期240卷 1221-1227页

作者： Stachowiak, Tomasz Szydlowski, Marek Jagiellonian Univ Astron Observ PL-30244 Krakow Poland Copernicus Ctr Interdisciplinary Studies PL-30387 Krakow Poland Jagiellonian Univ Marc Kac Complex Syst Res Ctr PL-30059 Krakow Poland

We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so-called continuous type, where the rate of expansion of perturbations is obtained for all times, and the exponents are reached as the limit at infinity. It does not involve exponentially divergent quantities so there is no need of rescaling or realigning of the solution. We show the algorithm's advantages and drawbacks using mainly the example of a particle moving between two contracting walls. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Lyapunov exponents numerical algorithm Highly oscillatory systems

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Determination of physical and geometrical characteristics of layered inhomogeneous elastic medium

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JOURNAL OF INVERSE AND ILL-POSED PROBLEMS 2011年第8期18卷 895-915页

作者： Bogulskii, I. O. Volchkov, Yu. M. Russian Acad Sci Inst Computat Modelling Siberian Branch Krasnoyarsk 660036 Russia Russian Acad Sci Lavrentiev Inst Hydrodynam Siberian Branch Novosibirsk 630090 Russia Novosibirsk State Univ Novosibirsk 630090 Russia

The article contains an exposition of the basic idea of construction of numerical algorithms based upon the several local approximations by linear polynomials for every sought-for function of dynamic problems of solids. We discuss also some problems of determination of physical and geometrical characteristics of layered inhomogeneous medium.

关键词： numerical algorithm decomposition scheme layered medium inverse problem

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Deep and near-surface consequences of root removal by asymmetric continental delamination

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TECTONOPHYSICS 2011年第1-2期502卷 257-265页

作者： Valera, J. L. Negredo, A. M. Jimenez-Munt, I. Univ Complutense Madrid Dept Geophys Fac Phys E-28040 Madrid Spain CSIC Inst Ciencias Tierra Jaume Almera E-08028 Barcelona Spain

The occurrence of continental delamination has been proposed for a number of areas characterized by highly variable geodynamic settings. In this study we present results of numerical simulations considering different initial setups, representative for geodynamic scenarios where delamination could potentially develop. To mimic a post-collisional orogenic scenario we have designed an initial state characterized by the presence of an area of orogenic lithosphere, with both crustal and lithospheric roots. In a second setup, we have considered a lithospheric root representative of a remnant slab with a flat overlying crust. We focus on predicted evolution of surface and near-surface observables, namely the crustal structure, surface heat flow and isostatic and dynamic topography evolution. Our results show that a high density orogenic lower crust, likely related to the presence of eclogite, significantly accelerates the sinking of the lithospheric mantle. The pattern of local isostatic elevation is characterized by laterally migrating surface uplift/subsidence. This pattern is shown to be little sensitive to lower crust density variations. In contrast, predicted dynamic topography is more sensitive to these changes, and shows surface subsidence adjacent to the delaminating lithospheric mantle for the model with a high density lower crust, and surface uplift above the slab for a model with a less dense lower crust. The reason for uplift in this second model is that the effect of the positive buoyancy of the thickened crust overwhelms the effect of negative buoyancy of the slowly sinking lithospheric mantle. We infer from our modeling that there is not a specific characteristic pattern of topography changes associated with delamination, but it depends on the interplay between highly variable factors, as slab sinking velocity, asthenospheric upwelling and changes in crustal thickness. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Continental delamination Topography evolution Thermo-mechanical modeling numerical algorithm

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On nonlinear fractional Klein-Gordon equation

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SIGNAL PROCESSING 2011年第3期91卷 446-451页

作者： Golmankhaneh, Alireza K. Golmankhaneh, Ali K. Baleanu, Dumitru Univ Pune Dept Phys Pune 411007 Maharashtra India Islamic Azad Univ Dept Phys Urmia Branch Oromiyeh Iran Islamic Azad Univ Dept Phys Mahabad Branch Mahabad Iran Cankaya Univ Dept Math & Comp Sci TR-06530 Ankara Turkey Inst Space Sci Magurele 76900 Romania

numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.

关键词： Caputo fractional derivative Fractional Klein Gordon Homotopy perturbation method numerical algorithm Iteration method

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Perturbation, extraction and refinement of invariant pairs for matrix polynomials

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LINEAR ALGEBRA AND ITS APPLICATIONS 2011年第3期435卷 514-536页

作者： Betcke, Timo Kressner, Daniel Swiss Fed Inst Technol Seminar Appl Math Zurich Switzerland Univ Reading Dept Math Reading RG6 2AH Berks England

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Polynomial eigenvalue problem Invariant pairs numerical algorithm Perturbation theory

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Analysis and algorithms for the computation of the excited states of helium

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第8期235卷 2041-2062页

作者： Ding, Zhonghai Chen, Goong Univ Nevada Dept Math Sci Las Vegas NV 89154 USA Texas A&M Univ Dept Math College Stn TX 77843 USA Texas A&M Univ Inst Quantum Studies College Stn TX 77843 USA

In this paper, we study a dimensionally scaled helium atom model for excited states of helium. The mathematical analysis of the corresponding effective energy potential is presented. Two simple numerical algorithms are developed for the computation of the excited states of helium. Comparison between our numerical results and those in the existing literature is given to indicate the accuracy and efficiency of the proposed algorithms. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Helium atom Schrodinger equation Excited states Dimensional scaling numerical algorithm

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