Prof. Dr. Mikael Mortensen - Automating the Spectral Galerkin Method - High Performance Computing in Python

Department of Mathematics, University of Oslo, Norway

Abstract

The spectral Galerkin method employs globally supported spectral basis functions (e.g., Fourier, Chebyshev, Legendre) in the Galerkin approximation. Due to its accuracy, the method is often favored in the study of fundamental physical phenomena in Cartesian domains, like turbulence and transitional flows. Until now there have been few tools available for solving PDEs with this method, at least not if one is aiming at high performance supercomputers. With the shenfun Python module (https://github.com/spectralDNS/shenfun) an effort is made towards automating the implementation of the spectral Galerkin method for simple (yet large in scale) tensor product domains. The user interface to shenfun is intentionally made very similar to FEniCS (https://fenicsproject.org). PDEs are represented through weak variational forms and solved using efficient, order optimal direct solvers, that are made possible by exploiting the structure of the operators (e.g., tri-/penta-diagonality and upper Hessenberg), that arise from clever choices of modified Chebyshev or Legendre bases. MPI decomposition is achieved through the recently released mpi4py-fft module (https://bitbucket.org/mpi4py/mpi4py-fft), and all developed solver may, with no additional effort, be run on supercomputers using thousands of processors. The shenfun package has, for example, been used to create Navier Stokes solvers for triply periodic domains as well as channels. This talk will give a demonstration of current capabilities and highlight Python as the powerful language it is for high performance scientific computing.

Dr. Sebastien Boyaval - Modelling Micro-Structured Flows : Recent Results, and Application to Viscoelastic Fluids

Laboratoire d'hydraulique Saint-Venant, Ecole des Ponts ParisTech, France

Abstract

Prof. Dr. Francisco Chinesta - Hybrid-Twins: When Data-Driven Mechanics Joins Advanced Model Order Reduction to Define Real-Time Dynamic Data-Driven Application Systems

Department of Computational Mechanics, École Centrale de Nantes, France

Abstract

In the previous (third) industrial revolution digital twins (able to emulate a physical system from the accurate solution of the mathematical model expected describing it) were major protagonists, making accurate analyses and designs possible. Numerical simulation is nowadays present in most of scientific fields and engineering domains, making possible the virtual evaluation of systems responses and alleviating the number of experiences on the real system that the numerical model represents. However, usually, virtual models (digital twins) are static, that is, they are used in the analysis and/or design of complex systems, but they are not expected to accommodate or assimilate data so as to define dynamic data-driven application systems. The characteristic time of standard simulation strategies is not compatible with the real-time constraints compulsory for control purposes or augmented reality environments.

Moreover, in practice, significant deviations between the predicted and observed responses are noticed, limiting the use of digital twins in many applications requiring online adaptation. In that situation control-based approaches were and are usually retained, in which the system is condensed into a goal-oriented transfer-function for which, despite of its effectiveness, the amount of information manipulated remains quite limited to do not compromise the compulsory real-time feedback.

The origin of the just referred deviations between predictions and measurements is due to (i) inaccuracies in the employed models that sometimes continue to be crude approximations/descriptions of the real systems; (ii) to the fact that in many cases models evolve in time in an “a priori" almost unpredictable manner; and (iii) inaccuracies in the determination of the model parameters or in their time-evolution.

Thus, nowadays, it is generally accepted the urgent need of more reliable modeling approaches as well as the dynamic assimilation of collected data on running simulations, for defining efficient Dynamic Data-Driven Application Systems - DDDAS. DDDAS consist of three main ingredients: (i) a simulation core able to solve complex mathematical or data-driven models under real-time constraints; (ii) advanced strategies able to assimilate data; and (iii) a mechanism to adapt the model online to evolving environments (that could imply the model change and not only the change of the parameters that an “a priori" assumed model involves). Hybrid-Twin embraces these three functionalities into a new paradigm in simulation-based engineering, and more concretely a cyber-physical-system framework.

Prof. Dr. Juan Miguel Nóbrega - Computational Rheology and Polymer Processing at the University of Minho

Department of Polymer Engineering, University of Minho, Portugal

Abstract

Nowadays, aiming an efficient use of resources, the advantages of employing numerical modelling tools to assist any design activity are consensual. Therefore, there are countless modelling software packages available, both commercial and open-source, which can be used to study extremely complex systems.

In the past, the open-source numerical codes presented very specific/limited capabilities and were developed by small research teams. Nowadays, some communities that develop and work with open-source codes are substantially enlarged and better organised. Hence, given the large range of skills covered by the development teams, some of these open-source codes cover a very wide range of applications. One successful case of this type is the OpenFOAM^® computational library, which can model complex multiphysics systems, covering both fluid and solid behaviours, being fully parallelized. One of the main advantages of OpenFOAM^® is its adaptiveness, resorting to a symbolic programming language, that allows a straightforward development of new applications for the resolution of specific problems, not available on the distributed releases.

This talk will begin with a brief presentation of the OpenFOAM^® computational library, its main features and capabilities. Then, several ongoing/recent case studies in the frame of computational rheology, polymer processing and related applications will illustrate its potential.

The International Conference on Computational Engineering (ICCE), which takes place from Thursday, September 28, to Friday, September 29, 2017, provides a meeting place for researchers and practitioners working on computational methods in all disciplines of engineering and applied mathematics, with a special focus on doctoral researchers and young scientists. The aim of the conference is to discuss the state of the art in this challenging field, develop promising perspectives for future research and initiate cooperations.

The conference is organized by the Graduate School of Computational Engineering (GSC CE) at TU Darmstadt together with the International Graduate School of Science and Engineering (IGSSE) at Technical University of Munich, the Stuttgart Research Center for Simulation Technology (SimTech) at University of Stuttgart and the Aachen Institute for Advanced Study in Computational Engineering Science (AICES) at RWTH Aachen University.