During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

Digital twin can be defined as a virtual representation of a physical asset enabled through data and simulators for real-time prediction, optimization, monitoring, controlling, and improved decision making. Recent advances in computational pipelines, multiphysics solvers, artificial intelligence, big data cybernetics, data processing and management tools bring the promise of digital twins and their impact on society closer to reality. Digital twinning is now an important and emerging trend in many applications. Also referred to as a computational megamodel, device shadow, mirrored system, avatar or a synchronized virtual prototype, there can be no doubt that a digital twin plays a transformative role not only in how we design and operate cyber-physical intelligent systems, but also in how we advance the modularity of multi-disciplinary systems to tackle fundamental barriers not addressed by the current, evolutionary modeling practices. In this work, we review the recent status of methodologies and techniques related to the construction of digital twins mostly from a modeling perspective. Our aim is to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.

/pdf/digital-twin-values-challenges-and-enablers-from-a-modeling-3hpoelaogn.pdf

Digital Twin: Values, Challenges and Enablers From a Modeling Perspective

The Functional Mockup Interface (FMI) is a tool independent standard for the exchange of dynamic models and for co simulation. The first version, FMI 1.0, was published in 2010. Already more than 30 tools support FMI 1.0. In this paper an overview about the recently published version 2.0 of FMI is given that combines the formerly separated interfaces for Model Exchange and Co-Simulation in one standard. Based on the experience on using FMI 1.0, many small details have been improved and new features ease the usability and increase the performance especially for larger models. Additionally, a free FMI compliance checker will become soon available and FMI models from different tools are made available on the web to simplify testing.

/pdf/functional-mockup-interface-2-0-the-standard-for-tool-4cimolga2r.pdf

Functional Mockup Interface 2.0: The Standard for Tool independent Exchange of Simulation Models

This article describes the Buildings library, a free open-source library that is implemented in Modelica, an equation-based object-oriented modelling language. The library supports rapid prototyping, as well as design and operation of building energy and control systems. First, we describe the scope of the library, which covers heating, ventilation and air-conditioning systems, multi-zone heat transfer and multi-zone airflow and contaminant transport. Next, we describe differentiability requirements and address how we implemented them. We describe the class hierarchy that allows implementing component models by extending partial implementations of base models of heat and mass exchangers, and by instantiating basic models for conservation equations and flow resistances. We also describe associated tools for pre- and post-processing, regression tests, co-simulation and real-time data exchange with building automation systems. The article closes with an example of a chilled water plant, with and without wate...

https://simulationresearch.lbl.gov/wetter/download/LBNL-1002944.pdf

Modelica Buildings Library

This document defines the Modelica language, version 1.4, which is developed by the Modelica Association, a non-profit organization with seat in Linkoping, Sweden. Modelica is a freely available, object-oriented language for modeling of large, complex, and heterogeneous physical systems. It is suited for multi-domain modeling, for example, mechatronic models in robotics, automotive and aerospace applications involving mechanical, electrical, hydraulic and control subsystems, process oriented applications and generation and distribution of electric power. Models in Modelica are mathematically described by differential, algebraic and discrete equations. No particular variable needs to be solved for manually. A Modelica tool will have enough information to decide that automatically. Modelica is designed such that available, specialized algorithms can be utilized to enable efficient handling of large models having more than hundred thousand equations. Modelica is suited and used for hardware-in-the-loop simulations and for embedded control systems.

Modelica - A Unified Object-Oriented Language for Physical Systems Modeling - Language Specification

The Functional Mockup Interface (FMI) is a tool independent standard for the exchange of dynamic models and for co-simulation. The development of FMI was initiated and organized by Daimler AG within the ITEA2 project MODELISAR. The primary goal is to support the exchange of simulation models between suppliers and OEMs even if a large variety of different tools are used. The FMI was developed in a close collaboration between simulation tool vendors and research institutes. In this article an overview about FMI is given and technical details about the solution are discussed.

https://www.ep.liu.se/ecp/063/013/ecp11063013.pdf

The Functional Mockup Interface for Tool independent Exchange of Simulation Models

Dymola is an integrated environment for developing models in the Modelica language. The growing use of Dymola has over time increased the demands on the development environment. Requests for extension and redesign originate from two sources: the need to simplify the use of Dymola to better support new and inexperienced users, and the need to better support "power users" which model extremely large and complex systems. Key areas in the development of Dymola are: a simplified and more coherent graphical user interface, browsing facilities for navigating large and complex systems, new experiment facilities for managing complex simulation tasks, distributed (parallel) simulation, and integrated version control to help manage model libraries and complete models. The paper describes the extensively redesigned Dymola 5, with an emphasis on new features compared to Dymola 4.

/pdf/dymola-for-multi-engineering-modeling-and-simulation-28icppkcgs.pdf

Dymola for Multi-Engineering Modeling and Simulation

SUMMARY
Co-simulation is a prominent method to solve multi-physics problems. Multi-physics simulations using a co-simulation approach have an intrinsic advantage. They allow well-established and specialized simulation tools for different fields and signals to be combined and reused with minor adaptations in contrast to the monolithic approach. However, the partitioned treatment of the coupled system poses the drawback of stability and accuracy challenges. If several different subsystems are used to form the co-simulation scenario, these issues are especially important. In this work, we propose a new co-simulation algorithm based on interface Jacobians. It allows for the stable and accurate solution of complex co-simulation scenarios involving several different subsystems. Furthermore, the Interface Jacobian-based Co-Simulation Algorithm is formulated such that it enables parallel execution of the participating subsystems. This results in a high-efficient procedure. Furthermore, the Interface Jacobian-based Co-Simulation Algorithm handles algebraic loops as the co-simulation scenario is defined in residual form. Copyright © 2014 John Wiley & Sons, Ltd.

Hans Olsson

Papers

The Functional Mockup Interface for Tool independent Exchange of Simulation Models

Functional Mockup Interface 2.0: The Standard for Tool independent Exchange of Simulation Models

Dymola for Multi-Engineering Modeling and Simulation

Interface Jacobian-based Co-Simulation

Interface-Jacobian based Co-Simulation