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Sökning: WFRF:(Claus Führer)

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  • Andersson, Christian, et al. (författare)
  • A Workbench for Multibody Systems ODE and DAE Solvers
  • 2012
  • Ingår i: Proceedings of the IMSD2012 - The 2nd Joint International Conference on Multibody System Dynamics. - 978-3-927618-32-9
  • Konferensbidrag (refereegranskat)abstract
    • During the last three decades, a vast variety of methods to numerically solve ordinary differential equations (ODEs) and differential algebraic equations (DAEs) has been developed and investigated. Few of them met industrial standards and even less are available within industrial multibody simulation software. Multibody Systems (MBS) offer a challenging class [5] of applications for these methods, since the resulting system equations are in the unconstrained case ODEs which are often stiff or highly oscillatory. In the constrained case the equations are DAEs of index-3 or less. Friction and impact in the MBS model introduce discontinuities into these equations while coupling to discrete controllers and hardware-in-the-loop components<br /> couple these equations to additional time discrete descriptions. Many of the developed numerical methods have promising qualities for these types of problems, but rarely got the chance to be tested on large scale problems. One reason is the closed software concept of most of the leading multibody system simulation tools or interface concepts with a high threshold to overcome. Thus, these ideas never left the academic environment with their perhaps complex but dimensionally low scale test problems. In this paper we will present a workbench, ASSIMULO, which allows easy and direct incorporation of new methods for solving ODEs or DAEs written in FORTRAN, C, Python or even MATLAB and which indirectly interfaces to multibody programs such as Dymola and Simpack, via a standardized interface, the functional mock-up interface. The paper is concluded with industrial relevant examples evaluated using industrial and academic solvers.
  • Andersson, Christian, et al. (författare)
  • Assimulo: A unified framework for ODE solvers
  • 2015
  • Ingår i: Mathematics and Computers in Simulation. - Elsevier. - 1872-7166 .- 0378-4754. ; 116, s. 26-43
  • Tidskriftsartikel (refereegranskat)abstract
    • During the last three decades, a vast variety of methods to numerically solve ordinary differential equations and differential algebraic equations has been developed and investigated. The methods are mostly freely available in different programming languages and with different interfaces. Accessing them using a unified interface is a need not only of the research community and for education purposes but also to make them available in industrial contexts. An industrial model of a dynamic system is usually not just a set of differential equations. The models today may contain discrete controllers, impacts or friction resulting in discontinuities that need to be handled by a modern solver in a correct and efficient way. Additionally, the models may produce an enormous amount of data that puts strain on the simulation software. In this paper, Assimulo is presented. It is a unified high-level interface to solvers of ordinary differential equations and is designed to satisfy the needs in research and education together with the requirements for solving industrial models with discontinuities and data handling. It combines original classical and modern solvers independent of their programming language with a well-structured Python/Cython interface. This allows to easily control parameter setting and discontinuity handling for a wide range of problem classes.
  • Andersson, Christian, et al. (författare)
  • Import and Export of Functional Mock-up Units in JModelica.org
  • 2011
  • Konferensbidrag (refereegranskat)abstract
    • Different simulation and modeling tools often use their own definition of how a model is represented and how model data is stored. Complications arise when trying to model parts in one tool and importing the resulting model in another tool or when trying to verify a result by using a different simulation tool. The Functional Mock-up Interface (FMI) is a standard to provide a unified model execution interface. In this paper we present an implementation of the FMI specification in the JModelica.org platform, where support for import and export of FMI compliant models has been added. The JModelica.org FMI import interface is written in Python and offers a complete mapping of the FMI C API. JModelica.org also offers a set of Pythonic convenience methods for interacting with the model in an object-oriented manner. In addition, a connection to the simulation environment Assimulo which is part of JModelica.org is offered to allow for simulation of models following the FMI specification using state of the art numerical integrators. Generation of FMI compliant models from JModelica.org will also be discussed.
  • Arévalo, Carmen, et al. (författare)
  • A collocation formulation of multistep methods for variable step-size extensions
  • 2002
  • Ingår i: Applied Numerical Mathematics. - Elsevier. - 0168-9274. ; 42:1-3, s. 5-16
  • Tidskriftsartikel (refereegranskat)abstract
    • Multistep methods are classically constructed by specially designed difference operators on an equidistant time grid. To make them practically useful, they have to be implemented by varying the step-size according to some error-control algorithm. It is well known how to extend Adams and BDF formulas to a variable step-size formulation. In this paper we present a collocation approach to construct variable step-size formulas. We make use of piecewise polynomials to show that every k-step method of order k + I has a variable step-size polynomial collocation formulation. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
  • Arévalo, Carmen, et al. (författare)
  • Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs
  • 2000
  • Ingår i: Applied Numerical Mathematics. - North-Holland. - 0168-9274. ; 35:4, s. 293-305
  • Tidskriftsartikel (refereegranskat)abstract
    • There are several approaches to using nonstiff implicit linear multistep methods for solving certain classes of semi-explicit index 2 DAEs. Using β-blocked discretizations (Arevalo et al., 1996) Adams-Moulton methods up to order 4 and difference corrected BDF (Soderlind, 1989) methods up to order 7 can be stabilized. As no extra matrix computations are required, this approach is an alternative to projection methods.Here we examine some variants of β-blocking. We interpret earlier results as regular β-blocking and then develop singular β-blocking. In this nongeneric case the stabilized formula is explicit, although the discretization of the DAE as a whole is implicit. We investigate which methods can be stabilized in a broad class of implicit methods based on the BDF ρ polynomials. The class contains the BDF, Adams-Moulton and difference corrected BDF methods as well as other high order methods with small error constants. The stabilizing difference operator&lt;space&gt;τ is selected by a minimax criterion for the moduli of the zeros of σ+τ. The class of explicit methods suitable as β-blocked methods is investigated. With singular β-blocking, Adams-Moulton methods up to order 7 can be stabilized with the stabilized method corresponding to the Adams-Bashforth methods.
  • Arnold, Martin, et al. (författare)
  • Numerical methods in vehicle system dynamics: state of the art and current developments
  • 2011
  • Ingår i: Vehicle System Dynamics. - Taylor & Francis. - 0042-3114 .- 1744-5159. ; 49:7, s. 1159-1207
  • Tidskriftsartikel (refereegranskat)abstract
    • Robust and efficient numerical methods are an essential prerequisite for the computer based dynamical analysis of engineering systems. In vehicle system dynamics, the methods and software tools from multibody system dynamics provide the integration platform for the analysis, simulation and optimization of the complex dynamical behaviour of vehicles and vehicle components and their interaction with hydraulic components, electronical devices and control structures.<br /> Based on the principles of classical mechanics, the modelling of vehicles and their components results in nonlinear systems of ordinary differential equations (ODEs) or differential-algebraic equations (DAEs) of moderate dimension that describe the dynamical behaviour in the frequency range required and with a level of detail being characteristic of vehicle system dynamics. Most practical problems in this field may be transformed to generic problems of numerical mathematics like systems of nonlinear equations in the (quasi-)static analysis and explicit ODEs or<br /> DAEs with a typical semi-explicit structure in the dynamical analysis. This transformation to mathematical standard problems allows to use sophisticated, freely available numerical software that is based on well approved numerical methods like the Newton-Raphson iteration for nonlinear equations or Runge-Kutta and linear multistep methods for ODE/DAE time integration.<br /> Substantial speed-ups of these numerical standard methods may be achieved exploiting some specific structure of the mathematical models in vehicle system dynamics.<br /> In the present paper, we follow this framework and start with some modelling aspects being relevant from the numerical viewpoint. The focus of the paper is on numerical methods for static and dynamic problems including software issues and a discussion which method fits best for which class of problems. Adaptive components in state-of-the-art numerical software like stepsize and order control in time integration are introduced and illustrated by a well known benchmark problem from rail vehicle simulation.<br /> Over the last few decades, the complexity of high-end applications in vehicle system dynamics has frequently given a fresh impetus for substantial improvements of numerical methods and for the development of novel methods for new problem classes. In the present paper, we address three of these challenging problems of current interest that are today still beyond the mainstream of numerical mathematics: (i) Modelling and simulation of contact problems in multibody dynamics, (ii) Real-time capable numerical simulation techniques in vehicle system dynamics and<br /> iii) Modelling and time integration of multidisciplinary problems in system dynamics including co-simulation techniques.
  • Diaz, José, et al. (författare)
  • A wavelet semidiscretisation of elastic multibody systems
  • 2003
  • Ingår i: Zeitschrift für Angewandte Mathematik und Mechanik. - John Wiley & Sons Ltd. - 0044-2267 .- 1521-4001. ; 83:10, s. 677-689
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we consider a coupled system of elastic and rigid bodies. It can be mathematically formulated as a coupled system of ordinary and partial differential equations, often written in its weak form. The discretisation is performed by a Galerkin-type ansatz in connection with a finite element approach or known eigenfunctions. Here, we demonstrate instead the use of a recently published Galerkin-wavelet method and its application to obtain a reasonable,small number of elastic modes.
  • Eich, Edda, et al. (författare)
  • On the error control for multistep methods applied to ODEs with invariants and DAEs in multibody dynamics
  • 1995
  • Ingår i: Mechanics of Structures and Machines. - 1525-612X .- 0890-5452. ; 23:2, s. 159-180
  • Tidskriftsartikel (refereegranskat)abstract
    • A modified local error model is developed for numerical integration of ODEs with invariants. The basic idea is to use a commutativity relationship that holds for implicit state-space form methods. A new implicit state-space form predictor is developed from which error estimates can be obtained by predictor-corrector difference: This technique is demonstrated through the preliminary examples in this paper.
  • Eich-Soellner, Edda, et al. (författare)
  • Numerische Methoden in der Mehrkörperdynamik
  • 1995
  • Ingår i: Mathematik in der Praxis: Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin. - Springer. - 978-3540592945 ; s. 41
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