Prof. Ignacio Grossmann, Ph.D. - Advances in Nonlinear Mixed-integer and Generalized Disjunctive Programming and Applications to the Optimization of Engineering Systems

Department of Chemical Engineering, Carnegie Mellon University, USA

Abstract

In this seminar, we first review recent advances in MINLP (Mixed-Integer Nonlinear Programming) and GDP (Generalized Disjunctive Programing) algorithms. We first describe the quadratic outer-approximation algorithm in which scaled second order approximations that provide valid bounds are incorporated into the master problem in order to reduce the number of major iterations in highly nonlinear convex MINLP problems. Applications are presented in safety layout problems, and in reliability design problems. Here the goal is to determine the number of standby units in serial systems with units that have pre-specified probabilities of failure, with the objectives being to minimize cost and to maximize availability. We apply the proposed models to the design of reliable air separation plants. We next address global optimization of nonconvex GDP problems for which bounds of the global optimum are strengthened through basic steps for the convex GDP approximations, and for which a logic based algorithm is proposed that relies on the use of cutting planes to avoid the increased dimensionality due to the use of hull relaxations. We illustrate the application of this algorithm to the optimal multiperiod blending problem for crude oil. We also address a nonconvex GDP problem corresponding to the design of centralized and distributed facilities. Given the number and location of suppliers and markets, the goal is to determine the number of facilities and their location in a two-dimensional space so as to minimize investment and transportation costs. We develop a special purpose method to solve this GDP problem and apply it to the design of biomass network facilities.

Prof. Dr. Holger Fröhlich - From Hype to Reality: Data Science Enabling Innovation in Biomedicine

Bonn-Aachen International Center for Information Technology (B-IT), University of Bonn, Germany

Abstract

Recent years have witnessed a dramatic increase of interest in Data Science and Artificial Intelligence in biomedical and pharmaceutical research. This increasing interest is accompanied by an often uncritical and hype generating debate in the main stream media, which is driven by a lack of understanding, hence pointing out the necessity for better education.

My talk will be divided into two parts: In the first part I want clarify terminology and give a general introduction into Data Science by briefly explaining some of the commonly used concepts. The second part will focus on the impact of Data Science in biomedical research. In particular, I want to demonstrate this connection by selected examples from own work. I will conclude my talk by reflecting on the strength and limitations of data driven modeling approaches and how future developments may help to overcome them.

Prof. Alessandro Reali, Ph.D. - Isogeometric Analysis: An Introduction and Some Recent Advances

Department of Civil Engineering and Architecture - Structures and Materials Section, University of Pavia, Italy

Abstract

Isogeometric Analysis (IGA) is a recent simulation framework, originally proposed by T.J.R. Hughes and coworkers in 2005, to bridge the gap between Computational Mechanics and Computer Aided Design (CAD). The basic IGA paradigm consists of adopting the same basis functions used for geometry representations in CAD systems - such as, e.g., Non-Uniform Rational B-Splines (NURBS) - for the approximation of field variables, in an isoparametric fashion. This leads to a cost-saving simplification of the typically expensive mesh generation and refinement processes required by standard finite element analysis. In addition, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per-degree-of-freedom and an enhanced robustness with respect to standard finite elements in a number of applications ranging from solids and structures to fluids, opening also the door to geometrically flexible discretizations of higher-order partial differential equations in primal form, as well as to highly efficient (strong-form) collocation methods.
The first part of this short course is devoted to the introduction of the basic concepts of IGA (including a brief primer on B-Splines and NURBS). The unique potential of IGA is then shown through some convincing applications, mainly belonging to the field of structural mechanics and of fluid-structure interaction, where the superior results that can be provided by IGA with respect to standard finite elements are clearly pointed out. 
The lecture is finally concluded by a brief presentation of further IGA works in progress and new ideas.

Prof. Dr. Laura De Lorenzis - Phase-Field Modeling and Computation of Fracture

Institute of Applied Mechanics, Technische Universität Braunschweig, Germany

Abstract

The phase-field modeling approach to fracture, after the pioneering investigations of the early 2000 in the mathematics community, has recently attracted a tremendous interest also in the engineering community due to its theoretical soundness, computational flexibility and demonstrated predictive power. In the talk, we review the basic ingredients of the classical phase-field model of brittle fracture and highlight the consequences of different modeling choices on the predicted behavior. We then illustrate the basic features of phase-field models for ductile fracture and finally overview the latest extensions and applications of the framework.

Prof. Dr. Inga Berre - Three-Dimensional Numerical Modelling of Hydraulic Stimulation of Geothermal Reservoirs: Permeability Enhancement and Induced Seismicity

Department of Mathematics, University of Bergen, Norway

Abstract

Understanding the controlling mechanisms underlying injection‐induced seismicity is important for optimizing reservoir productivity and addressing seismicity‐related concerns related to hydraulic stimulation in Enhanced Geothermal Systems as well as other sub-surface engineering applications. Hydraulic stimulation enhances permeability through elevated pressures, which cause normal deformations and the shear slip of preexisting fractures.

The process involves strongly coupled physical processes, involving reactivation and deformation of fractures, deformation of surrounding rock, and fluid flow in the fractures and their surroundings. The talk presents an approach for modelling of the governing flow and mechanics, where fractures are modelled as surfaces with associated apertures in a three-dimensional domain. Considering both flow and deformation, processes in the fractures are coupled with processes in the surrounding rock. While flow is assumed to be governed by Darcy’s law both in the fractures and the matrix, the model for deformation is inherently different for the fractured and non-fractured parts of the domain. Fracture reactivation is based on a Mohr-Coulomb criterion, and the corresponding irreversible deformation is based on an empirical model for friction.
Furthermore, fractures may continuously deform in the normal direction according to a non-linear model accounting for the normal loading. For the rock surrounding the matrix, we assume a continuous elastic deformation. Numerical results are presented to show how the methodology can be applied to understand important mechanisms affecting permeability and induced seismicity. In particular, we show how normal closure of fractures enhances pressure propagation away from the injection region and significantly increases the potential for postinjection seismicity.