Thursday, July 16. 2015
V.V. Aristov, A.A. Frolova, S.A. Zabelok
Dorodnicyn Computing Centre of Russian Academy of Sciences Vavilova str., 40, 119333, Moscow, Russia
Abstract: Simulations of flows on the basis of kinetic equations for mixtures with chemical reactions are performed. The Nonuniform Relaxation Problems (NRP) are formulated and solved. Unified Flow Solver (UFS) is used for 1D and 2D NRP. The nonequilibrium kinetics provides results outside the traditional theory of macroscopic phenomena based on the NavierStokes equations. Nonequilibrium flows with different properties in relaxation zones are described. Complex processes including model anabolic and catabolic chemical reactions are also considered.
Keywords: Boltzmann equation, kinetic chemical reactions, the nonuniform relaxation problem Mathematics Subject Classification: 76P05, 82C40 PACS: 05.20.Dd, 47.45.Ab, 51.10.+y
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Thursday, July 16. 2015
Lokendra K. Balyan^{a,1}, Subir Singh Lamba^{b}
^{a,b}Department of Mathematics, IIITDM Jabalpur, India ^{1}Corresponding author: Email: lokendra.balyan@gmail.com
Abstract: In this paper, we present rate of convergence estimates for eigenvalues and eigenvectors of elliptic differential operators on nonsmooth domains using nonconforming spectral element methods. We define a class of compact operators on Banach space which is used to obtain the results. If coefficients of the differential operator are sufficiently smooth and the boundaries of the polygonal domain are piecewise analytic then exponential convergence to approximate solution is obtained.
Keywords: Rate of convergence; eigenvalues and eigenvectors; nonsmooth domains; singularities; $h$$p$ spectral element method.
MSC: 35Jxx; 35Pxx
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Saturday, October 5. 2013
Luisa D’Amore^{2}, Valeria Mele^{a} and Almerico Murli^{b} ^{a}University of Naples Federico II, Naples, ITALY, ^{b}Southern Partnership for Advanced Computational Infrastructures (SPACI), c/o University of Naples, Federico II, Naples and CMCC  Centro EuroMediterraneo per i Cambiamenti Climatici, Lecce, ITALY Received 29 October, 2012; accepted in revised form 24 April, 2013
Abstract: A detailed rounding errors analysis for the computation of Taylor expansion coefficients of an analytic real function with respect to one variable, as implemented by TADIFF, a software package written in C++ specialized for computing Taylor expansion coefficients using Algorithmic Differentiation, is performed. The error analysis is carried out in a finite precision arithmetic system satisfying the IEEE standard 754. Furthermore, time and space complexity of such a computation is discussed. Experimental results aimed to validate both the accuracy and the complexity estimates are presented.
Keywords: Algorithmic Differentiation, Taylor expansion coefficients, TADIFF Mathematics Subject Classification: AMS: 65G50; 65Y20; 68Q25
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Monday, February 11. 2013
L. D’Amore^{1} , R. Arcucci^{2} , L. Marcellino^{3} and A. Murli^{2} 1. Department of Mathematics and Application, University of Naples Federico II, Italy. 2. Centro EuroMediterraneo per i Cambiamenti Climatici (CMCC), Italy. 3. Department of Applied Sciences, University of Naples Parthenope, Italy. Received 30 January, 2012; accepted in revised form 22 December, 2012 Abstract: The most significant features of Data Assimilation (DA) are that both the models and the observations are very large and nonlinear (of order at least O(108 )). Further, DA is an illposed inverse problem. Such properties make the numerical solution of DA very difficult so that, as stated in [19], ”solving this problem in ”realtime” it is not always pos sible and many different approximations to the basic assimilation schemes are employed”. Thus, the exploitation of advanced computing environments is mandatory, reducing the computational cost to a suitable turnaround time. This activity should be done according to a codesign methodology where software requirements drive hardware design decisions and hardware design constraints motivate changes in the software design to better fit within those constraints. In this paper, we address high performance computation issues of the three dimensional DA scheme underlying the oceanographic 3DVAR assimilation scheme, named Ocean VAR, developed at CMCC (Centro Euro Mediterraneo per i Cambiamenti Climatici), in Italy. The aim is to develop a parallel software architecture which is able to effectively take advantage of the available high performance computing resources. c 2012 European Society of Computational Methods in Sciences, Engineering and Technology
keywords: Data Assimilation, Inverse Problem, Parallel Software, Oceanography MSC: 65Y05, 65F22, 65Z05 PACS: 02.30.Zz
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Wednesday, January 16. 2013
Devendra Kumar, M.K. Kadalbajoo Received 5 August, 2011; accepted in revised form 22 July, 2012 Abstract: This paper is devoted to the numerical study for a class of boundary value problems of secondorder differential equations in which the highest order derivative is multiplied by a small parameter ǫ and both the convection and reaction terms are with negative shift. To obtain the parameteruniform convergence, a piecewise uniform mesh (Shishkin mesh) is constructed, which is dense in the boundary layer region and coarse in the outer region. Parameteruniform convergence analysis of the method has been given. The method is shown to have almost secondorder parameteruniform convergence. The effect of small delay δ on the boundary layer has also been discussed. To demonstrate the performance of the proposed scheme several examples having boundary layers have been carried out. The maximum absolute errors are presented in the tables.
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Wednesday, January 16. 2013
V. Ruas, A.P. Brasil, J.H. Carneiro de Araujo
Received 14 December, 2010; accepted in revised form 25 April, 2012 Abstract: A threefield finite element scheme designed for solving systems of partial dif ferential equations governing stationary viscoelastic flows is studied. It is based on the simulation of a timedependent behavior. Once a classical timediscretization is performed, the resulting threefield system of equations allows for a stable approximation of velocity, pressure and extra stress tensor, by means of continuous piecewise linear finite elements, in both two and three dimension space. This is proved to hold for the linearized form of the system. An advantage of the new formulation is the fact that it implicitly provides an algo rithm for the iterative resolution of system nonlinearities. Convergence in an appropriate sense applying to these three flow fields is demonstrated.
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Friday, June 22. 2012
Carla M.A. Pinto2 *,Cristina P. Santos**, Diana Rocha*, Vitor Matos** * Instituto Superior de Engenharia do Porto and Centro de Matematica da Universidade do Porto Rua Dr Antonio Bernardino de Almeida, 431, 4200072 Porto, Portugal ** Dept. Electronica Industrial and Centro Algoritmi Universidade do Minho Campus de Azurem 4800058 Guimaraes, Portugal Received 30 January, 2011; accepted in revised form 19 June, 2012 Abstract: There has been considerable development in the design of efficient controllers for trajectory follow ing in articulated robots with many degreesoffreedom. Nevertheless generating trajectories online is still a complex and unsatisfactorily solved problem. In this paper we present a new architecture for a Central Pattern Generator (CPG), for online generation of trajectories in quadruped robots. Our model is based on a CPG model for locomotor rhythms of quadruped animals, proposed by Golubitsky, Stewart, Buono, and Collins. Their model consists of eight coupled cells (CPG units) and each CPG unit is modeled as an oscillator by a system of ordinary differential equations (ODEs). We generalize their CPG model, considering that each cell or CPG unit is divided in rhythmic and discrete motor primitives, modeled by simple nonlinear systems of ODEs. Superposition of discrete and rhythmic primitives may allow for more complex motor behaviours, namely locomotion in irregular terrain and obstacle avoidance. In this paper, the discrete primitive is inserted into the rhythmic one (i) as an offset of the solution, (ii) summed to the solution of the rhythmic primitive. We also consider three types of couplings between CPG units: synaptic, diffusive and mixed. In this article we try to tackle the impact that these discrete corrections may have in the achieved system solu tions. Numerical results show that amplitude and frequency of the periodic solutions are almost constant for all couplings in cases (i) and (ii). The larger variation occurs in the values of amplitude and frequency for case (i) in the synaptic coupling. Results are also obtained in a robotic experiment using a simulated AIBO robot that walks over a ramp. Am plitude and frequency may be identified, respectively, with the range of motion and the velocity of the robots’ movement.
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Friday, June 22. 2012
Carla M.A. Pinto2 *, Diana Rocha*, Cristina P. Santos** * Instituto Superior de Engenharia do Porto and Centro de Matematica da Universidade do Porto Rua Dr Antonio Bernardino de Almeida, 431, 4200072 Porto, Portugal ** Universidade do Minho Dept. Electronica Industrial Campus de Azurem 4800058 Guimaraes, Portugal Received 29 December, 2011; accepted in revised form 19 June, 2012 Abstract: Humanoid robots have been extensively studied in the last few years. The motivation for this study is that bipedal locomotion is superior to wheeled approaches on real terrain and situations where robots accompany or replace humans. Some examples are, on the development of human assisting device, such as prosthetics, orthotics, and devices for rehabilitation, rescue of wounded troops, maidens, accompany and assistance to elderly people, amongst others. Online generation of trajectories for these robots is a complex process, that includes different types of movements, i.e., distinct motor primitives. In this paper, we consider two motor primitives: rhythmic and discrete. We study the effect on a bipeds robots’ gaits of inserting the discrete part as an offset of the rhythmic primitive, for synaptic and diffusive couplings. We also study stability of biped gaits. We simulate a periodic solution corresponding to the biped run, for the variation of the discrete offset. We find that amplitude and frequency of this periodic solution, are almost constant in all cases studied. This is useful when considering implementations of the proposed controllers for generating trajectories for the joints of real biped robots.
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Friday, June 22. 2012
Carla M.A. Pinto*, Diana Rocha*, Cristina P. Santos** * Instituto Superior de Engenharia do Porto and Centro de Matematica da Universidade do Porto Rua Dr Antonio Bernardino de Almeida, 431, 4200072 Porto, Portugal ** Universidade do Minho Dept. Electronica Industrial Campus de Azurem 4800058 Guimaraes, Portugal Received 9 December, 2011; accepted in revised form 19 June, 2012 Abstract: Legged robots are often used in a large variety of tasks, in different environments. The large number of degreesoffreedom, to be controlled during these tasks, turns the online generation of trajectories in these robots very complex. In this paper, we consider a modular approach to online generation of trajectories, based on biological concepts, namely Central Pattern Generators (CPGs). We introduce a new CPG model for hexapod robots’ rhythms, that generalizes the work of Golu bitsky, Stewart, Buono and Collins (1998,1999). Each neuron/oscillator in the CPG consists of two modules/primitives: rhythmic and discrete, that are modeled by nonlinear dynamical systems. Su perposition of discrete and rhythmic primitives permits the modeling of complex motor behaviors, namely locomotion in irregular terrain and obstacle avoidance. We study the effect on the amplitude and frequency of the robots’ gaits of superimposing the two motor primitives. The discrete primi tive is inserted as an offset of the solution of the rhythmic primitive. We also consider three types of couplings between CPG units: synaptic, diffusive and mixed. Simulation results reveal interesting facts, in certain cases amplitude and frequency of periodic solutions, identified with hexapods’ tripod, caterpillar and metachronal gaits, remain constant. Therefore, it is possible to use these solutions to generate trajectories for the joint values of real sixlegged robots, since varying the joint offset will not affect the required amplitude and frequency of the resultant trajectory nor the gait.
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Friday, June 22. 2012
O. Koch Institute for Analysis and Scientific Computing (E101), Vienna University of Technology, Wiedner Hauptstrasse 8–10, A1040 Wien, Austria Received 6 February, 2009; accepted in revised form 20 December, 2011 Abstract: We discuss the numerical approximation of the solution to the multi configuration timedependent HartreeFock (MCTDHF) equations in quantum dynamics. The associated equations of motion, obtained via the Dirac–Frenkel timedependent varia tional principle, consist of a coupled system of lowdimensional nonlinear partial differential equations and ordinary differential equations. We extend the analysis of the convergence of a time integrator based on splitting of the vector field for systems of unbound fermions to the case where a nuclear attractive potential is present. First order convergence in the H 1 norm and second order convergence in L2 are established. The analysis applies to electronic states whose density vanishes at the nucleus.
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Monday, June 18. 2012
J. Morais2 Freiberg University of Mining and Technology, Institute of Applied Analysis, Prueferstr. 9, 09596 Freiberg, Germany Received 26 November, 2010; accepted in revised form 28 July, 2011 Abstract: During the past few years considerable attention has been given to the role played by monogenic functions in approximation theory. The main goal of the present paper is to construct a complete orthogonal system of monogenic polynomials as solutions of the Riesz system over prolate spheroids in R3 . This will be done in the spaces of square integrable functions over R. As a first step towards is that the orthogonality of the polynomials in question does not depend on the shape of the spheroids, but only on the location of the foci of the ellipse generating the spheroid. Some important properties of the system are briefly discussed.
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Monday, June 18. 2012
E. Mainar and Juan Manuel Pena Departamento de Matematica Aplicada, Universidad de Zaragoza, Zaragoza, Spain Received 15 December, 2009; accepted in revised form 18 October, 2011 Abstract: We analyze some properties of bivariate tensor product bases. In particular, we obtain conditions so that a general bivariate tensor product basis is optimally stable for evaluation. Finally, we apply our results to prove the optimal stability of tensor product normalized Bbases.
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Monday, June 18. 2012
C. Dagnino , V. Demichelis Department of Mathematics, Faculty of Scienze Matematiche Fisiche e Naturali, University of Torino, 10100 Torino, Italy Received 30 January, 2009; accepted in revised form 13 October, 2011 Abstract: We propose a new quadrature rule for Cauchy principal value integrals based on quadratic spline quasiinterpolants which have an optimal approximation order and satisfy boundary interpolation conditions. In virtue of these spline properties, we can prove uniform convergence for sequences of such quadratures and provide uniform error bounds. A computational scheme for the quadrature weights is given. Some numerical results and comparisons with other spline methods are presented.
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Monday, June 18. 2012
Luigi Brugnano and Alessandra Sestini Dipartimento di Matematica “U. Dini” Viale Morgagni 67/A, 50134 Firenze, Italy Dedicated to Prof. D. Trigiante on the occasion of his 65th birthday. Received 16 December, 2009; accepted in revised form 24 September, 2011 Abstract: We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the numerical solution of freesurface problems. In particular, we here study their application to the numerical solution of both the (linear) parabolic obstacle problem and the obstacle problem. We propose a class of effective semiiterative Newtontype methods to find the exact solution of such piecewise linear systems. We prove that the semiiterative Newtontype methods have a global monotonic convergence property, i.e., the iterates converge monotonically to the exact solution in a finite number of steps. Numerical examples are presented to demonstrate the effectiveness of the proposed methods.
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Monday, June 11. 2012
Karline Soetaert Centre for Estuarine and Marine Ecology, Netherlands Institute of Ecology, 4401 NT Yerseke, The Netherlands
Thomas Petzoldt Institut fur Hydrobiologie Technische Universitat Dresden 01062 Dresden, Germany Received 21 February, 2011; accepted in revised form 11 March, 2011 Abstract: The opensource problem solving software R [1] has become one of the most widely used systems for statistical data analysis. As it is a powerful interpreted language, it is also very well suited for other disciplines in scientific computing. One of the fields where considerable progress has been made is the solution of differential equations. In this paper we describe a set of recently developed tools, socalled Rpackages, to efficiently solve and analyze initial value problems of differential equations in R. Most of the methods are based on welltested opensource numerical codes, combining the robustness and efficiency of these codes with the flexibility of the R language. We exemplify the use of these tools by several examples. We start by implementing a wellknown test problem for nonstiff solvers, the Arenstorff orbit ordinary differential equations. Next we solve the pendulum problem, a DAE of index 3. A description of a bouncing ball shows how roots and events can be programmed in R. After that we describe how to implement delay differential equations, which we exemplify with a DDE that is subject to an impulse, triggered at specific times. We end with a rather stiff partial differential equation, a combustion problem modeled in 2D. The presented R packages provide additional facilities to efficiently plot the outcome, to compare different scenarios, to estimate summary statistics, or to display execution statistics that help in assessing the performance of a particular method.
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