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Analysis of non-autonomous linear ODE systems in bifurcation problems via lie group geometric numerical integrators 1

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International conference on Dynamical Systems: theory and applications, DSTA 2015

作者： Foti, Pilade Fraddosio, Aguinaldo Marzano, Salvatore Piccioni, Mario Daniele Dipartimento di Scienze dell’Ingegneria Civile e dell’Architettura Politecnico di Bari Bari Italy

ISBN: (数字)9783319424088

ISBN: (纸本)9783319424071

A bifurcation analysis developed within the context of the nonlinear theory of elasticity usually leads to the study of systems of second-order ODE’s characterized by matrices with varying coefficients. A common practice is that of reducing the governing set of differential equations to a simpler non-autonomous first order linear ODE system. Here, we investigate the potentiality of alternative geometric numerical integrators, based on Lie Group methods, which furnish approximate exponential representations of the matricant of first order linear ODE systems. Within such numerical schemes, the Magnus expansion seems to be very efficient since it features the determination of approximate solutions that preserve at any order of approximation the same qualitative properties of the exact (but unknown) solution and it also exhibits an improved accuracy with respect to other frequently used numerical schemes. As applications of the Magnus method, we study certain paradigmatic bifurcation problems with the major aim of investigating whether solid bodies may support certain instabilities that have common features to some classical hydrodynamic instabilities observed in viscous fluids. © Springer International Publishing Switzerland 2016.

关键词： Lie groups

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Approximation of Periodic PDE Solutions with Anisotropic Translation Invariant Spaces

Approximation of Periodic PDE Solutions with Anisotropic Tra...

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International conference on Sampling theory and applications

作者： Ronny Bergmann Dennis Merkert Department of Mathematics University of Kaiserslautern

ISBN: (纸本)9781538615669

We approximate the quasi-static equation of linear elasticity in translation invariant spaces on the torus. This unifies different FFT-based discretisation methods into a common framework and extends them to anisotropic lattices. We analyse the connection between the discrete solution spaces and demonstrate the numerical benefits. Finite element methods arise as a special case of periodised Box spline translates.

关键词： Solution space approximation linear elasticity Invariant Anisotropy Translations Translation Translation Process Solutions Periodic

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numerical Mathematics and Advanced applications 2009: Proceedings of Enumath 2009, the 8th European conference on numerical Mathematics and Advanced applications, Uppsala, July 2009

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2016年

作者： Gunilla Kreiss Per Lötstedt Axel Målqvist Maya G Neytcheva Per L Tstedt Axel M Lqvist

ISBN: (纸本)9783662519530

The European conference on numerical Mathematics and Advanced applications (ENUMATH) was held from June 29-July 3, 2010, in Uppsala, Sweden. This was the eighth conference in a series of biannual meetings starting in Paris (1995). S- sequent conferences were organized in Heidelberg (1997), Jyvas ] kyla ] (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), and Graz (2007). ENU- MATH 2009 attracted over 330 attendees to the scienti c programme, with ten invited speakers, one public lecture, 32 minisymposia, and more than 280 presen- tions. This volume contains a selection of papers by the invited speakers and from the minisymposia and the contributed sessions. The purpose of the conference was to create a forum for discussion and d- semination of recent results in numerical mathematics and new applications of computational methods. Many subjects were covered in the talks and a few of the topicsrepresentedin these proceedingswere discontinuousGalerkinmethods, nite elementmethodsindifferentapplications, methodsfor uid ow, electromagnetism, nancial engineering, structuralmechanics, optimalcontrol, andbiomechanics. The minisymposia listed below with their organizers also give an impression of how broad the scope of the conference was: Adaptivity for non-linearand non-smooth problems, part I & II, Ralf Kornhuber, Andreas Veeser Advanced techniques in radial basis function approximation for PDEs, partI & II, Natasha Flyer, Elisabeth Larsson Advances in numerical methods for non-Newtonian ?ows, part I & II, Erik Burman, Maxim Olshanskii, Stefan Turek Anisotropicadaptivemeshes: erroranalysisandapplications, partI&II, Thierry Coupez, Simona Perotto Asymptotic linear algebra, numerical methods, and applications, part I & II, Marco Donatelli, Stefano Serra-Capizzano Biomechanics, part I & II, Gerhard A.

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Green computing on graphics processing units

Green computing on graphics processing units

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4th International Workshop on Embedded Multicore Computing and applications in conjunction with the 16th IEEE International conference on High Performance and Communications

作者： Magoules, Frederic Ahamed, Abal-Kassim Cheik Suzuki, Atsushi CentraleSupelec F-92295 Chatenay Malabry France

To answer the question 'How much energy is consumed for a numerical simulation running on Graphic Processing Unit?', an experimental protocol is here established. The current provided to a graphic processing unit (GPU) during computation is directly measured using amperometric clamps. Signal processing on the intensity of the current of the power supplied to a GPU, with noise reduction technique, gives precise timing of GPU states, which allow establishing an energy consumption model of the GPU. Energy consumption of each operation, memory copy, vector addition, and element wise product is precisely measured to tune and validate the energy consumption model. The accuracy of the proposed energy consumption model compared to measurements is finally illustrated on a conjugate gradient method for a problem discretized by a finite element method. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： Green computing GPU CUDA Alinea Cusp linear algebra sparse matrix-vector product iterative methods conjugate gradient compressed sparse row format

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Hi-BoX: A generic library of fast solvers for boundary element methods

Hi-BoX: A generic library of fast solvers for boundary eleme...

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IEEE conference on Antenna Measurements & applications (CAMA)

作者： Toufic Abboud Denis Barbier IMACS Ecole Polytechnique Palaiseau Cedex FRANCE

ISBN: (纸本)9781467389334

Hi-BoX is a generic library implementing state-of-the-art fast direct and iterative solvers for existing codes based on Boundary Element Method (BEM) or Method of Moments (MoM). It benefits from recent advances in numerical methods, linear algebra and High Performance Computing (HPC). This includes new advances in H-matrix and Fast Multipole Method (FMM) and their hybridization, new approaches for handling a large number of right-hand sides, and finally the use of new parallelization techniques based on a runtime system simplifying the use of modern massively parallel and heterogeneous architectures.

关键词： Kernel Libraries linear algebra Transmission line matrix methods Runtime numerical models Method of moments

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Operator-theoretic approach to minimal-norm bandlimited interpolation of nonuniform samples

Operator-theoretic approach to minimal-norm bandlimited inte...

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International conference on Sampling theory and applications

作者： Nguyen T. Thao Dominik Rzepka Dept. of EE City College of New York CUNY Dept. of Electronics AGH Univ. of Science and Tech.

ISBN: (纸本)9781538615669

methods for the minimal-norm bandlimited inter-polation of nonuniform samples are known to have serious numerical issues even though this interpolation is mathematically well defined. Moreover, they have been formulated only for finite numbers of samples. By a rigorous revisit of this problem from an operator-theoretic viewpoint in Hilbert spaces, we devise an algorithm for this interpolation that applies to an infinite number of samples with no condition, with guaranteed stability at least for finite numbers of samples, and with a recursive part that can be rigorously implemented in discrete time.

关键词： Nonuniform sampling Bandlimited signals Interpolation Minimal norm Least squares Algorithm stability linear operator Pseudoinverse Frame

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Widely linear quaternion adaptive filtering in the frequency domain

Widely linear quaternion adaptive filtering in the frequency...

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International conference on Mathematical methods in Electromagnetic theory (MMET)

作者： Francesca Ortolani Aurelio Uncini Dpt. of Information Engineering Sapienza University of Rome Rome Italy

ISBN: (纸本)9781509019571

Adaptive filtering can be expanded to new numerical systems and unseen sides of physical problems can be highlighted thanks to the mathematical properties of such hypercomplex algebras. Each algebra has its own rules and operation results may not be compatible from one algebra to another. However, such peculiarities diversify algebras in a way that each of them fits specific geometrical/physical problems. In this work we propose a quaternion widely linear adaptive algorithm operating in the frequency domain. The aim is to overcome the problem of high computational cost occurring when time-domain algorithms are used. An analysis of the cost is also supplied. Finally, simulations support our proposal.

关键词： Quaternions algebra Frequency-domain analysis Time-domain analysis Transforms Computational efficiency Covariance matrices

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On preconditioned iteration methods for complex linear systems

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JOURNAL OF ENGINEERING MATHEMATICS 2015年第1期93卷 41-60页

作者： Bai, Zhong-Zhi Chinese Acad Sci Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp State Key Lab Sci Engn Comp Beijing 100190 Peoples R China

A complex system of linear equations arises in many important applications. We further explore algebraic and convergence properties and present analytical and numerical comparisons among several available iteration methods such as C-to-R and PMHSS for solving such a class of linear systems. Theoretical analyses and computational results show that reformulating a complex linear system into an equivalent real form is a feasible and effective approach, for which we can construct, analyze, and implement accurate, efficient, and robust preconditioned iteration methods.

关键词： Complex symmetric linear system Convergence theory PMHSS iteration Preconditioning Real reformulation Spectral properties

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Convergence theory of exact interpolation scheme for computing several eigenvectors

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numerical linear algebra WITH applications 2016年第2期23卷 373-390页

作者： Pultarova, I. Charles Univ Prague Fac Math & Phys Math Inst Sokolovska 83 Prague 18675 8 Czech Republic Czech Tech Univ Fac Civil Engn Dept Math Thakurova 7 Prague 16629 6 Czech Republic

An asymptotic convergence analysis of a new multilevel method for numerical solution of eigenvalues and eigenvectors of symmetric and positive definite matrices is performed. The analyzed method is a generalization of the original method that has recently been proposed by R. Kuel and P. Vanek (DOI: 10.1002/nla.1975) and uses a standard multigrid prolongator matrix enriched by one full column vector, which approximates the first eigenvector. The new generalized eigensolver is designed to compute eigenvectors. Their asymptotic convergence in terms of the generalized residuals is proved, and its convergence factor is estimated. The theoretical analysis is illustrated by numerical examples. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： numerical computation of eigenvalues and eigenvectors multilevel methods Rayleigh quotient convergence rate

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The oscillator with linear and cubic elastic restoring force and quadratic damping 1

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International conference on Dynamical Systems: theory and applications, DSTA 2015

作者： Marinca, V. Herişanu, N. University Politehnica Timişoara Bd.Mihai Viteazu Nr.1 Timişoara300222 Romania Center for Advanced and Fundamental Technical Research Romanian Academy Timisoara Branch Bd. M.Viteazu Nr.24 Timişoara300223 Romania

ISBN: (数字)9783319424088

ISBN: (纸本)9783319424071

A novel analytic approximate technique, namely optimal variational method (OVM), is employed to propose an approach to solve some nonconservative nonlinear oscillators. Different from perturbation methods, the validity of the OVM is independent on whether or not there exist small physical parameters in the considered nonlinear equations. This procedure offers a promising approach by constructing a generalized Lagrangian and a generalized Hamiltonian for nonlinear oscillators. An excellent agreement has been found between the analytical results obtained by the proposed method and numerical integration results. © Springer International Publishing Switzerland 2016.

关键词： Nonlinear equations

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