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A Coupled Finite Difference - Gaussian Beam Method for High Frequency Wave Propagation

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Workshop on Numerical Analysis and Multiscale Computations

作者： Tanushev, Nicolay M. Tsai, Yen-Hsi Richard Engquist, Bjoern Univ Texas Austin Dept Math Austin TX 78712 USA

ISBN: (纸本)9783642219429

Approximations of geometric optics type are commonly used in simulations of high frequency wave propagation. This form of technique fails when there is strong local variation in the wave speed on the scale of the wavelength or smaller. We propose a domain decomposition approach, coupling Gaussian beam methods where the wave speed is smooth with finite difference methods for the wave equations in domains with strong wave speed variation. In contrast to the standard domain decomposition algorithms, our finite difference domains follow the energy of the wave and change in time. A typical application in seismology presents a great simulation challenge involving the presence of irregularly located sharp inclusions on top of a smoothly varying background wave speed. These sharp inclusions are small compared to the domain size. Due to the scattering nature of the problem, these small inclusions will have a significant effect on the wave field. We present examples in two dimensions, but extensions to higher dimensions are straightforward.

关键词： Gaussian beams

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Some Remarks on Eigenvalue Approximation by Finite Elements

Some Remarks on Eigenvalue Approximation by Finite Elements

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12th LMS-EPSRC Summer School in computational Mathematics and Scientific Computation

作者： Boffi, Daniele Gardini, Francesca Gastaldi, Lucia Univ Pavia Dipartmento Matemat Via Ferrata 1 I-27100 Pavia Italy Univ Brescia Dipartimento Matemat I-25133 Brescia Italy

ISBN: (纸本)9783642239144;9783642239137

The aim of this paper is to supplement the results of Boffi (Acta Numer. 19:1-120, 2010) with some additional remarks. In particular we deal with three distinct topics: we review some tutorial examples in one dimension and provide numerical codes for them;we analyze the case of multiple eigenvalues and show some numerical;we review a posteriori error analysis for eigenvalue problems.

关键词： Eigenvalues and eigenfunctions

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Some Remarks on Free Energy and Coarse-Graining

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Workshop on Numerical Analysis and Multiscale Computations

作者： Legoll, Frederic Lelievre, Tony Univ Paris Est CERMICS Ecole Ponts ParisTech 6 & 8 Ave Blaise Pascal F-77455 Marne La Vallee 2 France Univ Paris Inst Navier LAMI F-77455 Paris France

ISBN: (纸本)9783642219429

We present recent results on coarse-graining techniques for thermodynamic quantities (canonical averages) and dynamical quantities (averages of path functionals over solutions of overdamped Langevin equations). The question is how to obtain reduced models to compute such quantities, in the specific case when the functional to be averaged only depends on a few degrees of freedom. We mainly review, numerically illustrate and extend results from (Blanc et al. Journal of Nonlinear science 20(2):241-275, 2010;Legoll and Lelievre Nonlinearity 23(9):213l-2163, 2010.), concerning the computation of the stress-strain relation for one-dimensional chains of atoms, and the construction of an effective dynamics for a scalar coarse-grained variable when the complete system evolves according to the overdamped Langevin equation.

关键词： Free energy

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Introduction to Applications of Numerical Analysis in Time Domain computational Electromagnetism

Introduction to Applications of Numerical Analysis in Time D...

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12th LMS-EPSRC Summer School in computational Mathematics and Scientific Computation

作者： Chen, Qiang Monk, Peter Univ Delaware Dept Math Sci Newark DE 19716 USA

ISBN: (纸本)9783642239144;9783642239137

We discuss two techniques for the solution of the time domain Maxwell system. The first is a partial differential equation based approach using conforming finite elements and implicit time stepping that is suitable when stiff problems are encountered, and where the medium is inhomogeneous. In particular we analyze the use of edge elements and certain A-stable schemes using the Fourier-Laplace transform. For a homogeneous medium, an integral equation approach can be used and we describe and analyze the convolution quadrature method applied to the electric field integral equation. In either case we emphasize that the convergence analysis depends on energy estimates for the continuous problem.

关键词： Convolution

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Native handling of message-passing communication in data-flow analysis 1

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6th International Conference on Automatic Differentiation, AD 2012

作者： Pascual, Valérie Hascoët, Laurent INRIA Sophia-Antipolis France

ISBN: (数字)9783642300233

ISBN: (纸本)9783642300226

Automatic Differentiation by program transformation uses static data-flow analysis to produce efficient code. This data-flow analysis must be adapted for parallel programs with Message-Passing communication. Starting from a context-sensitive and flow-sensitive data-flow analysis scheme initially devised for sequential codes, we extend this scheme for parallel codes. This extension is independent of the particular analysis and does not require a modification of the code's internal representation, i.e. the flow graph. This extension relies on an accurate matching of communication points, which can't be found automatically in general, and thus new user directives prove useful. © 2012 Springer-Verlag.

关键词： Message passing

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Combining automatic differentiation methods for high-dimensional nonlinear models 1

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6th International Conference on Automatic Differentiation, AD 2012

作者： Reed, James A. Utke, Jean Abdel-Khalik, Hany S. Department of Nuclear Engineering North Carolina State University Raleigh NC United States Argonne National Laboratory University of Chicago Chicago IL United States

ISBN: (数字)9783642300233

ISBN: (纸本)9783642300226

Earlier work has shown that the efficient subspace method can be employed to reduce the effective size of the input data stream for high-dimensional models when the effective rank of the first-order sensitivity matrix is orders of magnitude smaller than the size of the input data. Here, the method is extended to handle nonlinear models, where the evaluation of higher-order derivatives is important but also challenging because the number of derivatives increases exponentially with the size of the input data streams. A recently developed hybrid approach is employed to combine reverse-mode automatic differentiation to calculate first-order derivatives and perform the required reduction in the input data stream, followed by forward-mode automatic differentiation to calculate higher-order derivatives with respect only to the reduced input variables. Three test cases illustrate the viability of the approach. © 2012 Springer-Verlag.

关键词： Input output programs

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Using directed edge separators to increase efficiency in the determination of Jacobian matrices via automatic differentiation 1

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6th International Conference on Automatic Differentiation, AD 2012

作者： Coleman, Thomas F. Xiong, Xin Xu, Wei Department of Combinatorics and Optimization University of Waterloo Waterloo ON N2L 3G1 Canada Department of Mathematics Tongji University Shanghai 200092 China

ISBN: (数字)9783642300233

ISBN: (纸本)9783642300226

Every numerical function evaluation can be represented as a directed acyclic graph (DAG), beginning at the initial input variable settings, and terminating at the output or corresponding function value(s). The "reverse mode" of automatic differentiation (AD) generates a "tape" which is a representation of this underlying DAG. In this work we illustrate that a directed edge separator in this underlying DAG can yield space and time efficiency gains in the application of AD. Use of directed edge separators to increase AD efficiency in different ways than proposed here has been suggested by other authors (Bischof and Haghighat, Hierarchical approaches to automatic differentiation. In: Berz M, Bischof C, Corliss G, Griewank A (eds) computational differentiation: techniques, applications, and tools, SIAM, Philadelphia, PA, pp 83-94, 1996;Bücker and Rasch, ACM Trans Math Softw 29(4):440-457, 2003). In contrast to these previous works, our focus here is primarily on space. Furthermore, we explore two simple algorithms to find good directed edge separators, and show how these ideas can be applied recursively to great advantage. Initial numerical experiments are presented. © 2012 Springer-Verlag.

关键词： Jacobian matrices

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Applying automatic differentiation to the community land model 1

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6th International Conference on Automatic Differentiation, AD 2012

作者： Mametjanov, Azamat Norris, Boyana Zeng, Xiaoyan Drewniak, Beth Utke, Jean Anitescu, Mihai Hovland, Paul Mathematics and Computer Science Argonne National Laboratory 9700 South Cass Avenue Argonne IL 60439 United States Environmental Science Argonne National Laboratory 9700 South Cass Avenue Argonne IL 60439 United States

ISBN: (数字)9783642300233

ISBN: (纸本)9783642300226

Earth system models rely on past observations and knowledge to simulate future climate states. Because of the inherent complexity, a substantial uncertainty exists in model-based predictions. Evaluation and improvement of model codes are one of the priorities of climate science research. Automatic Differentiation enables analysis of sensitivities of predicted outcomes to input parameters by calculating derivatives of modeled functions. The resulting sensitivity knowledge can lead to improved parameter calibration. We present our experiences in applying OpenAD to the Fortran-based crop model code in the Community Land Model (CLM). We identify several issues that need to be addressed in future developments of tangent-linear and adjoint versions of the CLM. © 2012 Springer-Verlag.

关键词： Climate models

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Hierarchical algorithmic differentiation a case study 1

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6th International Conference on Automatic Differentiation, AD 2012

作者： Lotz, Johannes Naumann, Uwe Ungermann, Jörn Lehr- und Forschungsgebiet Informatik 12: Software and Tools for Computational Engineering RWTH Aachen University Aachen 52056 Germany Research Center Jülich GmbH Jülich 52425 Germany

ISBN: (数字)9783642300233

ISBN: (纸本)9783642300226

This case study in Algorithmic Differentiation (AD) discusses the semi-automatic generation of an adjoint simulation code in the context of an inverse atmospheric remote sensing problem. In-depth structural and performance analyses allow for the run time factor between the adjoint generated by overloading in C++ and the original forward simulation to be reduced to 3. 5. The dense Jacobian matrix of the underlying problem is computed at the same cost. This is achieved by a hierarchical AD using adjoint mode locally for preaccumulation and by exploiting interface contraction. For the given application this approach yields a speed-up over black-box tangent-linear and adjoint mode of more than 170. Furthermore, the memory consumption is reduced by a factor of 1,000 compared to applying black-box adjoint mode. © 2012 Springer-Verlag.

关键词： Jacobian matrices

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Using automatic differentiation to study the sensitivity of a crop model 1

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6th International Conference on Automatic Differentiation, AD 2012

作者： Lauvernet, Claire Hascoët, Laurent Le Dimet, François-Xavier Baret, Frédéric Irstea UR MALY 3 bis quai Chauveau - CP 220 Lyon F-69336 France INRA Avignon France INRIA Sophia-Antipolis France Université de Grenoble Grenoble France

ISBN: (数字)9783642300233

ISBN: (纸本)9783642300226

Automatic Differentiation (AD) is often applied to codes that solve partial differential equations, e.g. in geophysical sciences or computational Fluid Dynamics. In agronomy, the differentiation of crop models has never been performed since these models are more empirical than fully mecanistic, derived from equations. This study shows the feasibility of constructing the adjoint model of a crop model referent in the agronomic community (STICS) with the TAPENADE tool, and the use of this accurate adjoint to perform some sensitivity analysis. This paper reports on the experience from AD users of the environmental domain, in which AD usage is not very widespread. © 2012 Springer-Verlag.

关键词： Sensitivity analysis

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