| 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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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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| 3. |
- Arnold, Martin, et al.
(författare)
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Numerical methods in vehicle system dynamics: state of the art and current developments
- 2011
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Ingår i: Vehicle System Dynamics. - : Informa UK Limited. - 1744-5159 .- 0042-3114. ; 49:7, s. 1159-1207
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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. 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 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. Substantial speed-ups of these numerical standard methods may be achieved exploiting some specific structure of the mathematical models in vehicle system dynamics. 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. 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 iii) Modelling and time integration of multidisciplinary problems in system dynamics including co-simulation techniques.
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| 4. |
- Führer, Claus, et al.
(författare)
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Computing with Python
- 2013
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Description: Python® is a free open-source language and environment that has great potential in scientific computing. Computing with Python presents the programming language in close connection wit mathematical applications. The approach of the book is concept based rather than a systematic introduction to the language. It is written for a mathematical readership and is aimed at students with a mathematical background. Computing with Python can be used as a course book for absolute beginners on Python with guidance and support from a teacher. It is also suitable as a self study book for more advanced students with some programming knowledge and an interest in mathematical or scientific disciplines. The book integrates programming with mathematics and gives a systematic treatment of Python’s capabilities with application to scientific computing.
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| 5. |
- Smrekar, Jure, et al.
(författare)
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Methodology for evaluation of cooling tower performance - Part 2: Application of the methodology and computational aspects of Poppe equations
- 2011
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Ingår i: Energy Conversion and Management. - : Elsevier BV. - 0196-8904. ; 52:11, s. 3282-3289
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Tidskriftsartikel (refereegranskat)abstract
- A methodology for evaluation of natural draft cooling tower (CT) performance and its application is presented. The study establishes the connection between CT performance and power output. It can estimate a change in a CT’s efficiency as well as an increase in power output as a function of cooling water temperature and load to the plant. The methodology consists of three subparts, i.e. Cooling Tower Profiler (CTP) method, CT model and a model of the power plant that are described in the first part of the paper. The second part focuses on application of the methodology in a way that minimizes error of the CT model. One week of data from the power plant were acquired for the analysis. In the CT a small area with irregularities was examined, and increased efficiency and power output are estimated by the methodology. Furthermore, another aspect of solving Poppe equations is examined resulting in reduced computational effort by approximately a half without losing any computational accuracy.
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| 6. |
- Ylikiiskilä, Johan, et al.
(författare)
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Improving Newton's method for Initialization of Modelica models
- 2011
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Konferensbidrag (refereegranskat)abstract
- Initializing a model written in Modelica translates to finding consistent initial values to the underlying DAE. Adding initial equations and conditions creates a system of non-linear equations that can be solved for the initial configuration. This paper reports an implementation of Newton's method to solve the non-linear initialization system. This implementation also uses a regularization method to deal with singular Jacobians as well as sparse solvers to exploit the sparsity structure of the Jacobian. The implementation is based on the open-source projects JModelica.org and Assimulo, KINSOL from the SUNDIALS suite and SuperLU.
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