Abstract:
Open session.

Chair: Markus Bause (Helmut Schmidt University of the Federal Armed Forces Hamburg, Germany) and Florin Adrian Radu (University of Bergen, Norway)

Abstract:
Since recently there is an emerging interest in analyzing and simulating poromechanics that belongs to the classical but still largely unsolved problems. Poromechanics has challenging applications of practical interest covering many branches of science and technology, in particular, the geosciences (e.g. geothermal energy, oil and gas recovery, fracturing), environmental sciences (e.g. long-term disposal of waste, remediation of contaminated sites), mechanical engineering (e.g. vibro-acoustics and vehicle engineering) and the life sciences (e.g. biomechanis and medicine). Mathematical models for poromechanics are built upon the work of Biot and couple mechanical deformation with fluid flow. They involve non-linear, possible degenerate, systems of partial differential equations. This complicates their mathematical analyses and the design of efficient numerical schemes.

In this minisymposium recent advances in mathematical modelling of poromechanics as well as in the development of reliable discretization schemes and solver technology for the coupled systems are discussed. A special focus will be on problems with multiphase or reactive flow phenomena. Further, applications of practical relevance belong also to the scope of interest.

Chair: Klaus Kaiser (RWTH Aachen University, Germany) and Jochen Schütz (Universiteit Hasselt, Belgium)

Abstract:
Developing algorithms for singularly perturbed problems can be challenging. This is in particular true for problems of (near-)hyperbolic type. In this minisymposium, we discuss recent advances toward the treatment of those problems with the aid of schemes of mixed implicit / explicit (IMEX) type.

Chair: Peter Frolkovič (F.A. Universität Erlangen-Nürnberg)

Abstract:
In this minisymposium we shall discuss recent developments in the Level-set and Lagrangian computational methods for curve and surface evolutions and show their usage in various applications.

Chair: Thomas Henneron (Lille1 University, France) and Ruth V. Sabariego (KU Leuven, Belgium)

Abstract:
Model order reduction techniques are a trend topic in computational science and that due to the ever increasing demand of realistic simulations. We aim at accounting for multiple scales (in space and time), for multiple physical phenomena (mechanics, electromagnetism, thermal processes…), for multiple parameters in optimisation applications, for nonlinearities... with an acceptable computational cost in terms of time and memory storage. These techniques provide a compact model of a complex physical problem that captures its main features, i.e. a minimum number of unknowns but preserving a good accuracy. With this dedicated session, we would like to go through the current know-how in different model order reduction techniques (purely mathematical or physically based such as Reduced Basis, Proper Orthogonal Decomposition, Proper Generalized Decomposition, ...) applied at a system-level simulation but with a detailed design at component-level (structural mechanics, fluid mechanics, electromagnetism, thermal processes...).

Chair: Ivan Cimrák, Iveta Jančigová (University of Žilina, Žilina, Slovakia)

Abstract:
The rapidly evolving area of microarrays, or lab-on-chips, offers an enormous increase in efficiency of laboratory experiments. The miniaturization of the experiments with resolution of several micrometers allows for better control of the experiments. These microarrays have numerous advantages such as faster analysis and response times of the system, massive parallelization due to compactness, lower fabrication costs.

For the design of such microarrays, computational experiments can be effectively used. This symposium is devoted to topics that are related to the modelling of processes inside microfluidic channels.

We especially welcome contributions, which address the models of fluid-structure interactions and those which cover processes on micro-scales where tracking of individual cells is possible. This approach allows for understanding of behaviour of individual cells and for monitoring the cells under exposure to modulated flow. We also welcome other contributions that concern blood flow modelling, modelling other cells in fluid, modelling microfluidic devices, computational methods for cell tracking, characterisation and identification and other related topics.

Chair: Hendrik Rogier (Ghent University, Belgium)

Abstract:
In the last decades, we have seen tremendous advances in electromagnetic full-wave modelling techniques, up to such a scale that commercial electromagnetic field solvers based on integral equations, finite elements and finite differences have become fully integrated as computer-aided engineering tools in most design processes of complex electronic systems. Yet, very complex and very large problems still represent major obstacles for mainstream full-wave simulators, making the analysis of such structures highly time consuming and their computer-aided optimization impossible.

This mini-symposium provides an overview of the latest developments in electromagnetic field modelling research towards even more efficient and accurate solvers for large intricate simulation domains. Advanced preconditioning methods that avoid dense mesh and low frequency breakdown are presented, as well as local grid refinement techniques. In addition, the incorporation of stochastic frameworks into full-wave electromagnetic field solvers is discussed, including some pertinent design examples in the context of wearable antenna design.

Chair: Matteo Icardi (Warwick), Thomas Carraro (Heildelberg)

Abstract:
Charged particles and electrochemistry are present in a large number of important applications such as energy storage, automotive, consumer electronics, biological membranes. Here, a number of difficulties arise when coupling the fluid flow equations with electrostatic forces, electrochemical reactions, and porous structures. From the modelling perspective, due to the extreme complexity of the physics involved, depending on the scale of interest, many assumptions can be made, such as electro-neutrality, effective reaction rates, mean field approximations. Despite these assumptions the resulting PDE system is often non-linear and tightly coupled. The analysis of these equations and the development of robust numerical discretisation schemes are often challenging. Furthermore, issues like parametrisation, uncertainty and overall validity of the models at the different scales, make the actual simulation of these devices often not yet fully predictive.

This minisymposium aims at gathering researchers in several areas to present and share recent advances in
i) understanding appropriate modelling assumptions and valid micro-scale equations,
ii) deriving new model reduction and upscaling techniques,
iii) analysis of the arising PDE systems,
iv) developing numerical schemes and solvers,
v) applying simulation methodologies to real industrial cases

Chair: Abdellatif EL BADIA (University of Tecnnology of Colpiegne, France)

Abstract:
In various fields of science, engineering and bioengineering, many important problems can be formulated as inverse problems (IP) for partial differential equations. Among them, inverse source problems (ISP) which consist of determining external force terms, from additional informations (given data, measurements, observations) on the state of the corresponding to the direct problem. The inverse source problems have attracted great attention from many researchers over recent years of course of their applications to many practical examples, particularly in biomedical imaging techniques such as; electro-encephalography/magneto encephalography (EEG/MEG) problems, pollution in the environment, photo and thermo-acoustic tomography (PAT and TAT), bioluminescence and fluorescence.

One of the objectives of this minisymposia is to give an overview of the state of the art of the topic.

Chair: Serge Nicaise (Université de Valenciennes et du Hainaut Cambrésis, Laboratoire de Mathématiques et leurs Applications de Valenciennes, France)

Abstract:
The finite element method is widely used to solve time-harmonic Maxwell's systems. Today one of the challenges is to evaluate the quality of the solution with the help of error estimates. Hence different authors focus either on a priori estimates, where some regularity results on the exact solutions are required, or a posteriori error analysis, where only the energy regularity is requested. My goal is to invite different specialists on both topics in order to share their recent results.

Chair: Mohammad Issa (Groupe de Recherche en Electromagnétisme, LAPLACE, Toulouse)

Abstract:
During the past decade, the computational electromagnetics has evolved rapidly to a point where various alternative modeling approaches and numerical methods are available for very general problems. This progress is due to the wide range of applications like Electric motors, transformers, microwave heating, optical fibers and wave-guides, eddy current, and antennas, etc. In this symposium, we consider the modelisation of particular electromagnetic problems and structures, as well as the numerical methods that contribute in modeling and solving them.

Chair: Christophe Geuzaine (University of Liege)

Abstract:
Time-harmonic wave problems arise in a variety of scientific and industrial problems, with far reaching applications in domains as diverse as radar scattering from airplanes, medical imaging, electromagnetic compatibility, geophysical exploration or acoustic noise simulations. The underlying mathematical model for such problems is the Helmholtz equation. In recent years the need has arisen to solve very large-scale Helmholtz problems with billions of unknowns, for both (piecewise) homogeneous or inhomogeneous media. This minisymposium will showcase several recent approaches to tackle such challenging problems, both from a mathematical and from a computational point of view.

Chair: Rob De Staelen (Ghent University)

Abstract:
In recent decades, fractional calculus has found a large number of profound applications, which have triggered the development of methods for more reliable discretisation and approximations of the dynamics of continuous systems. From a pragmatic point of view, fractional order models provide better descriptions and, ultimately, a better understanding of underlying complex phenomena in sciences and technology. To that end, novel analytical methods to investigate qualitative features of the solutions of these nonlocal systems as well as more general results on the existence and the uniqueness of suitable solutions are desirable tools in the study of fractional systems.

At the same time, continuous models based on systems of partial differential equations have been investigated via various criteria of discretisation. Novel numerical methods to approximate the solutions of fractional systems have emerged in the literature. However, the search for discrete techniques which are faster and stable, which possess a higher order of convergence at lower computational costs, and which preserve the main features of the solutions of interest, is a constant pursuit in the numerical analysis. In particular, the design of discretisation of continuous fractional systems that preserve important characteristics, such as positivity, boundedness, convexity, monotonicity, and energy, is a fruitful area of research that merits a closer attention.

In light of these facts, the purpose of this mini-symposium is to present original high-quality research that address the latest progress on analytical methods of fractional systems or that analyse new numerical schemes for fractional differential equations arising in science and technology. Rather than mere applications of standard analytical and numerical techniques, our emphasis is on novel theoretical results and the analysis of new methodologies.