Title: Innovations for Future Modelica
Authors: Hilding Elmqvist, Toivo Henningsson and Martin Otter
Abstract:This paper discusses language innovations for future Modelica versions, on the one hand for generally applicable language elements, and on the other hand to improve modeling of multibody systems with contacts, and media modeling. In a companion paper new algorithms are proposed to handle much larger models than can be treated today. All these innovations are developed and evaluated with the experimental modeling and simulation environment Modia. Modia is based on Julia, a powerful programming language with strong focus on scientific computing, meta-programming and just-in-time compilation that allows very fast development. The modeling language is directly defined and implemented with Julia’s meta-programming constructs and is designed tightly together with the symbolic and numeric algorithms. This approach is very well suited for innovation and experimenting with evolutions of modeling capabilities in Modelica.
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Title: Transformation of Differential Algebraic Array Equations to Index One Form
Authors: Martin Otter and Hilding Elmqvist
Abstract:Several new algorithms are proposed that in effect transform DAEs (Differential Algebraic Equations) to a special index one form that can be simulated with standard DAE integrators. The transformation to this form is performed without solving linear and/or nonlinear equation systems, the sparsity of the equations is kept, and array equations remain array equations or differentiated versions of them. Furthermore, certain DAEs can be handled where structural index reduction methods fail. It is expected that these new algorithms will help to treat large Modelica models of any index in a better way as it is currently possible. The algorithms have been evaluated and tested in the experimental simulation environment Modia that is implemented with the Julia programming language.
Links: Full paper