| 1. |
- Andersson, Christian, et al.
(författare)
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A Workbench for Multibody Systems ODE and DAE Solvers
- 2012
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Ingår i: Proceedings of the IMSD2012 - The 2nd Joint International Conference on Multibody System Dynamics. - 9783927618329
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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 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.
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| 2. |
- Andersson, Christian, et al.
(författare)
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Assimulo: A unified framework for ODE solvers
- 2015
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Ingår i: Mathematics and Computers in Simulation. - : Elsevier BV. - 0378-4754. ; 116, s. 26-43
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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.
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| 3. |
- Andersson, Christian, et al.
(författare)
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Efficient Predictor for Co-Simulation with Multistep Sub-System Solvers
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- An industrial model of a dynamic system is usually not just a set of differential equations. External inputs acting on the system are common, such as an external force acting on a body or wind pressing on a car. Update of these inputs needs to be handled by the numerical solver in an efficient way.In dynamical simulation, multistep methods are commonly used. A multistep method uses the solution history in order to predict the future solution. When an input is changed, the history is no longer a good approximation for the future solution which may result in order reductions and simulation failure.In this paper, a modification of the predictor is presented. Modifying the predictor, instead of restarting the method, results in an increased performance of the method. The cost of the modification must be weighed with the cost of restarting the method. Experiments show that the benefit of modifying the predictor outweighs the cost of a restart.
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| 4. |
- Andersson, Christian, et al.
(författare)
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Import and Export of Functional Mock-up Units in JModelica.org
- 2011
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Ingår i: [Host publication title missing]. - 9789173930963
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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.
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| 5. |
- Andersson, Christian, et al.
(författare)
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PyFMI: A Python Package for Simulation of Coupled Dynamic Models with the Functional Mock-up Interface
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- With the advent of the Functional Mock-up Interface (FMI) standard, exchanging dynamic models between modeling and simulation tools has been greatly simplified. At the core of it, FMI is a standardized and unified model execution interface for dynamic models. FMI has gained widespread adoption among users and numerous commercial and open source tools implement support for the standard. In this article, the Python package PyFMI is introduced. PyFMI supports loading and execution of models compliant with the FMI standard, called Functional Mock-up Units (FMUs). It includes a master algorithm for simulation of coupled FMUs together with connections to both Assimulo, for simulation of single FMUs, and to SciPy, for performing parameter estimation. Accessing models compliant with FMI in Python, which is an open and accessible scripting language, is intended to further spread the standard and also promote and facilitate future development of the standard. This is due to Python being a convenient language for experimentation and prototyping of numerical algorithms. PyFMI is also demonstrated on a number of problems that highlights its viability for solving industrial grade simulation problems with FMUs.
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| 6. |
- Arévalo, Carmen, et al.
(författare)
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A collocation formulation of multistep methods for variable step-size extensions
- 2002
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Ingår i: Applied Numerical Mathematics. - 0168-9274. ; 42:1-3, s. 5-16
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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.
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| 7. |
- Arévalo, Carmen, et al.
(författare)
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Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs
- 2000
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Ingår i: Applied Numerical Mathematics. - 0168-9274. ; 35:4, s. 293-305
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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 operatorτ 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.
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| 8. |
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| 9. |
- Arévalo, Carmen, et al.
(författare)
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Stabilized multistep methods for index 2 Euler-Lagrange DAEs
- 1996
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Ingår i: BIT. - 0006-3835. ; 36:1, s. 1-13
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Tidskriftsartikel (refereegranskat)abstract
- We consider multistep discretizations, stabilized by β-blocking, for Euler-Lagrange DAEs of index 2. Thus we may use “nonstiff” multistep methods with an appropriate stabilizing difference correction applied to the Lagrangian multiplier term. We show that order p =k + 1 can be achieved for the differential variables with order p =k for the Lagrangian multiplier fork-step difference corrected BDF methods as well as for low order k-step Adams-Moulton methods. This approach is related to the recently proposed “half-explicit” Runge-Kutta methods.
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| 10. |
- Arévalo, Carmen, et al.
(författare)
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β-blocked multistep methods for Euler-Lagrange DAEs: Linear analysis
- 1997
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Ingår i: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. - : Wiley. - 0044-2267. ; 77:8, s. 609-617
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Tidskriftsartikel (refereegranskat)abstract
- Many different methods have been suggested for the numerical solution of index 2 and 3 Euler-Lagrange equations. We focus on 0-stability of multistep methods (φ, σ) and investigate the relations between some well-known computational techniques. By various modifications, referred to as β-blocking of the σ polynomial, some basic shortcomings of multistep methods may be overcome. This approach is related to projection techniques and has a clear and well-known analogy in control theory. In particular, it is not necessary to use BDF methods for the solution of high index problems; indeed, “nonstiff” methods may be used for part of the system provided that the state-space form is nonstiff. We illustrate the techniques and demonstrate the results with a simplified multibody model of a truck.
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