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Numerically Implemented Impact of a Femtosecond Laser Pulse on Glass in the Approximation of Nonlinear Maxwell Equations

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Mathematical Models and Computer Simulations 2020年第1期12卷 77-89页

作者： Zhukov, V.P. Fedoruk, M.P. Institute of Computational Technologies Siberian Branch Russian Academy of Sciences Novosibirsk 630090 Russian Federation Novosibirsk State Technical University Novosibirsk 630073 Russian Federation Novosibirsk State University Novosibirsk 630090 Russian Federation

Abstract: A finite-difference scheme is presented for the solution of the problem on the interaction of a femtosecond laser pulse with glass in the approximation of nonlinear Maxwell equations supplemented by equations of the hydrodynamic type for conduction electrons. The model takes into account all the basic physical processes involved in this interaction. An axially symmetric problem is considered. The construction of the scheme allows for the specifics of the problem, which ensures the efficiency of the developed method. The use of the scheme is illustrated by the results of modeling the interaction between glass and femtosecond laser pulses of an ordinary Gaussian shape with linear polarization and doughnut pulses with radial and azimuthal polarization. Significant differences in the dynamics of the interaction between glass and these three types of pulses are revealed. © 2020, Pleiades Publishing, Ltd.

关键词： aperture femtosecond laser pulse finite-difference scheme implicit algorithms Kerr effect nonlinear Maxwell equations plasma

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Static solution of crack propagation problems in Peridynamics

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019年 346卷 126-151页

作者： Ni, Tao Zaccariotto, Mirco Zhu, Qi-Zhi Galvanetto, Ugo Hohai Univ Coll Civil & Transportat Engn Nanjing 210098 Jiangsu Peoples R China Hohai Univ Key Lab Minist Educ Geomech & Embankment Engn Nanjing Jiangsu Peoples R China Univ Padua Ind Engn Dept Via Venezia 1 I-35131 Padua Italy Ctr Studies & Act Space CISAS G Colombo Via Venezia 15 I-35131 Padua Italy

The static solution of crack propagation problems can be an efficient way to find both the failure load of a structure and the shape of the crack pattern. The paper introduces two new implicit static solution procedures to study crack propagation problems by adopting a Peridynamic-based numerical tool, and compares them with the Sequentially Linear Analysis. We discretize the structures in space by adopting a coupled FEM-PD approach, which exploits the flexibility of FEM to reduce the overall computational cost of the simulation. The results of several numerical examples indicate the main novel conclusions of the paper: when using a PD-based software, controlling the maximum number of bonds broken in each iteration may increase significantly the accuracy of the solution and keep the computational cost to an acceptable level. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Static solution Fracture Peridynamics implicit algorithms Coupling approach Finite element method

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A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

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JOURNAL OF COMPUTATIONAL PHYSICS 2016年 326卷 763-772页

作者： Chacon, L. Stanier, A. Los Alamos Natl Lab Los Alamos NM 87545 USA

We demonstrate a scalable fully implicit algorithm for the two-field low-beta extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton-Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 x 4096 mesh, we demonstrate a wall-clock-time speedup of similar to 6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement. Published by Elsevier Inc.

关键词： implicit algorithms Extended MHD JFNK Physics-based preconditioning Parallel multigrid

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implicit computation of maximum bipartite matchings by sublinear functional operations

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THEORETICAL COMPUTER SCIENCE 2014年第P2期560卷 131-146页

作者： Bollig, Beate Gille, Marc Proeger, Tobias TU Dortmund Dortmund Germany ETH Inst Theoret Informat Zurich Switzerland

The maximum bipartite matching problem, an important problem in combinatorial optimization, has been studied for a long time. In order to solve problems for very large structured graphs in reasonable time and space, implicit algorithms have been investigated. Any object to be manipulated is binary encoded and problems have to be solved mainly by functional operations on the corresponding Boolean functions. OBDDs are a popular data structure for Boolean functions, therefore, OBDD-based algorithms have been used as a heuristic approach to handle large input graphs. Here, two OBDD-based maximum bipartite matching algorithms are presented, which are the first ones using only a sublinear number of operations (with respect to the number of vertices of the input graph) for a problem unknown to be in NC, the complexity class that contains all problems computable in deterministic polylogarithmic time with polynomially many processors. Furthermore, the algorithms are experimentally evaluated. (C) 2014 Elsevier B.V. All rights reserved.

关键词： implicit algorithms Maximum bipartite matchings Ordered binary decision diagrams

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On implicit algorithms of continuation method with applications to dynamic systems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2004年 164卷 207-224页

作者： Danilin, AN Snegovski, DV Volkov-Bogorodski, DB Univ Liege Inst Elect Montefiore B-4000 Liege Belgium RAS Inst Appl Mech Moscow Russia

In this work, we show that numerical solution of the Cauchy problem for a system of ODEs of the second order resolved with respect to the higher derivative can be obtained by constructing the simple and effective implicit step-by-step integration procedures without involving laborious iterative processes like Newton-Raphson. The problem is initially transformed to a new argument, an integral curve length. Such transformation involves one equation that relates the initial parameter of problem and integral curve length. Based on the linear acceleration method, we demonstrate a procedure of constructing an implicit algorithm, which uses simple iterations to numerically solve the transformed Cauchy problem. The definitions of computational properties of iterational process are formulated and proven. Explicit estimates of integration step providing the convergence of simple iterations are given. Effectiveness of the proposed method is demonstrated upon three problems solved with and without preliminary parameterisation. The problem of celestial mechanics "Pleiades" is considered as a test one. The second example deals with modelling nonlinear dynamic of elastic cantilever flexible beam, which is rolled in initial static state into a ring by the bending moment. In third example, we give a solution for deployment of mechanical system of three flexible beams under prescribed control laws. (C) 2003 Elsevier B.V. All rights reserved.

关键词： dynamic systems continuation method implicit algorithms simple iterations

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implicit extension of Taylor series method with numerical derivatives for initial value problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2005年第7期50卷 1167-1177页

作者： Miletics, E Molnárka, G Szechenyi Istvan Univ Dept Math Gyor Hungary

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of this algorithms is based on the approximate calculation of higher derivatives using well-known finite-difference technique for the partial differential equations. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval integration. This property offers different facility for adaptive error control. This paper describes several explicit Taylor series algorithms with numerical derivatives and their implicit extension and examines its consistency and stability properties. The implicit extension based on a collocation term added to the explicit truncated Taylor series and the approximate solution obtained as a continuously differentiable piecewise polynomials function. Some numerical test results is presented to prove the efficiency of these new-old algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： numerical derivatives finite differences implicit algorithms collocation methods

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implicit extension of Taylor series method with numerical derivatives for initial value problems

Implicit extension of Taylor series method with numerical de...

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9th International Conference on Numerical Methods and Computational Mechanics (NMCM2002)

作者： Miletics, E Molnárka, G Szechenyi Istvan Univ Dept Math Gyor Hungary

关键词： numerical derivatives finite differences implicit algorithms collocation methods

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Automatic correction of the time step in implicit simulations of the stamping process

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2004年第13-14期40卷 1995-2010页

作者： Oliveira, MC Menezes, LF Univ Coimbra Dept Mech Engn P-3030 Coimbra Portugal

A specific aspect of simulations of stamping processes is the numerical method adopted to include the non-linearities associated with the frictional contact problem in large deformation plasticity. In fact, convergence problems are frequently encountered, especially when using a quasi-static implicit algorithm. One way of increasing the numerical robustness of these algorithms is to adopt an augmented Lagrangian method to incorporate the problem of contact with friction. The resulting non-linear system can be solved by a Newton-Raphson type method, for which a trial solution must be given to start the iterative equilibrium loop. The quality of this trial solution is determinant for the convergence of the iterative process. An automatic control of the size of the time step can improve this trial solution. In this study, a new size control for the time step, imposing restrictions not only on the increments of the state variables but also on the increments of the contact forces, is proposed, An example of a bending test is used to analyse the influence of this new limitation on the overall convergence behaviour of the fully implicit code DD3IMP. (C) 2004 Elsevier B.V. All rights reserved.

关键词： finite element analysis implicit algorithms contact with friction

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A general tangent operator procedure for implicit elastoplastic BEM analysis

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2004年第5期6卷 431-439页

作者： Miers, LS Telles, JCF Fed Univ Rio De Janeiro COPPE Rio De Janeiro RJ Brazil

Most formulations involving the use of the so-called consistent elastoplastic tangent operator procedure, in boundary element analysis, have been presented taking in consideration only a J(2)-type yield criterion, like von Mises. The present paper aims at bringing a general consistency concept to tangent operators obtained without yield criterion particularization, ready to be used in implicit schemes for elastoplastic BEM analysis. The ideas follows much of the second author's physically nonlinear implicit BEM solution procedures introduced in the 80's and is based on a Taylor series expansion of the true effective stress around an equivalent stress corresponding to the accumulated true stresses up to, but not including, the current increment taken to be "elastic". To illustrate the efficiency of the technique, some comparative results using different yield criteria are presented.

关键词： elastoplasticity boundary elements implicit algorithms

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A general framework for conservative single-step time-integration schemes with higher-order accuracy for a central-force system

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2003年第33-34期192卷 3585-3618页

作者： Graham, E Jelenic, G Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2BY England

A general framework for algorithms that conserve angular momentum for single-body central-force problems is presented. It is shown that any family of momentum-conserving algorithms can have at most three free parameters, one of which may be used to ensure energy conservation (and hence will be configuration-dependent). Further restrictions can be made that enable the algorithms to recover the orbits of relative equilibria of the underlying physical problem. In addition, the algorithms can be made time-reversible, whilst still leaving two parameters unspecified. The order of accuracy of a general momentum-conserving family is analysed, and it is shown that energy-momentum algorithms that preserve the underlying physical relative equilibria can have unlimited accuracy if the two remaining parameters are appropriately chosen functions of the configuration and the time-step: this does not require any additional degrees of freedom, extra stages of calculation or information from past solutions. Numerical examples are given that show the performance of some representative higher-order schemes when applied to stiff and non-stiff problems, and the issue of Newton-Raphson convergence is discussed. (C) 2003 Elsevier B.V. All rights reserved.

关键词： non-linear dynamics higher-order accuracy conservation properties relative equilibria time reversibility non-unique solutions implicit algorithms

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