# HGS MathComp Curriculum & Events

## 2012/13 ws

**Compact Courses**

#### Introduction to molecular dynamics and coarse-grained modeling of biomolecules

**Date:**
2012-01-01 - 15:00

**Speaker:** Jörg Langowski, Jochen Erler

**Location:** DKFZ, TP3 building, INF 580 Seminar Room 4.101

**ECTS-Points:** 4

This course presents an overview over state-of-the art computer modelling and simulation techniques for large biomolecules, ranging from atomic detail to a global, coarse-grained description.

Basic knowledge in the structure and interactions of biological macromolecules are required

Please register here:

http://hgs.iwr.uni-heidelberg.de/Portfolio_HGS/VERANSTALTUNGEN/reg_form/reg_form.php?id=78

#### 3D-Analyse, 3D-Datengewinnung

**Date:**
2012-01-01 - 7:00

**Speaker:** Hubert Mara

**ECTS-Points:** 4

Data Acquisition with Laser Scanning Techniques

#### The fundamentals and recent twists to video processing []

**Date:**
2013-01-01 - 9:30

**Speaker:** Dr. Shai Avidan

**Location:** HCI, Speyerer Strasse 6, Monday Jan 28th - Friday Feb 1st from 09:30 to 12:30 am, in the large seminar room

**ECTS-Points:** 2

Contents

1) Lucas-Kanade and applications

Derive Lucas-Kanade optic flow equations. Show applications to super-resolution and video stabilization. Support Vector Tracking - show how to combine object detection and

tracking.

2) Horn-Schunck and extensions

Derive Horn-Schunck equations. Discuss the connections between H-S and MRF in general. Show recent work on SIFT-Flow for pixel labeling problems.

3) Tracking and representation

Tracking as inference problem. How to represent objects in tracking? (templates, histograms, classifiers, Locally Orderless patches).

4) Unsupervised Video segmentation

Background subtraction, shot detection, unsupervised video segmentation.

5) Supervised Video segmentation

Rotoscoping, scribbleBoost, video snapcut.

Shai Avidan http://www.eng.tau.ac.il/~avidan/ received the Ph.D. degree from the School of Computer Science, Hebrew University, Jerusalem,

Israel, in 1999. Currently, he is an Assistant Professor at the Faculty of Engineering, Tel-Aviv University, Tel-Aviv, Israel. In between he worked for Adobe, Mitsubishi Electric Research Labs (MERL) and Microsoft Research. He published extensively in the fields of object tracking in video and 3-D object modeling from images. He is also interested in Internet vision applications such as privacy preserving image analysis, distributed algorithms for image analysis, and image retargeting.

#### 3D Data Acquisition and Processing of Irregular Meshes with GigaMesh

**Date:**
2013-01-07 - 14:00

**Speaker:** Dr. Susanne Krömker / Hubert Mara

**Location:** Lectures: INF 368, room 532; practical: OMZ INF 250, U011

**ECTS-Points:** 3

3D data acquisition with structured light in high resolution will be presented with the Breuckmann smartSCAN 3D-HE scanner owned by the HGS MathComp. The postprocessing comprises the basic steps with the proprietary software OPTOCAT and the open source program MESHLAB for dealing with high resolution irregular meshes, and the generation and analysis of the high dimensional feature space with the program GigaMesh.

You will get the knowledge of how to

- acquire 3D surface data with structured light in high resolution

- do the postprocessing of building watertight 3D models (software training with OPTOCAT)

- deal with the open source program MESHLAB for 3D mesh reduction

- generate a high dimensional feature space of multiscale volume and surface integral invariants with GigaMesh

- learn about the mesh processing pipeline and 3D filter techniques

- analyze the feature space with various metrics

- visualize the results on the 3D model

- extract the information in vector format

The course is planned as a practical hands on course.

Please register here:

http://hgs.iwr.uni-heidelberg.de/Portfolio_HGS/VERANSTALTUNGEN/reg_form/reg_form.php?id=76

#### WebGL []

**Date:**
2013-01-24 - 11:00

**Speaker:** Dr. Susanne Krömker / Jens Schöbel

**Location:** OMZ, INF 350, Computerpool U011

**ECTS-Points:** 3

WebGL is a 3D-programming API directly provided by modern browsers. This enables you to develop 3D programs by just writing a simple HTML file plus a little bit of coding. In this course you will learn that _little bit of coding_.

You will get the fundamental knowledge of how to write your own WebGL program, how to use shaders and render it in your browser. My course will cover the following topics:

- Basic HTML and JavaScript coding

- How to write a simple WebGL program

- Object Oriented Programming in JavaScript

- Developing a (very) simple game engine using WebGL as renderer

- Fetching data via AJAX from a webserver

- Performance optimization via shader

The course is planned as a practical hands on course. The goal is that you are able to write your own WebGL shader and use JavaScript to access the render and store data.

For the course I assume that you have basic coding skills (you have written a program before and can do so again) and a good feeling for 3D math.

Please register here:

http://hgs.iwr.uni-heidelberg.de/Portfolio_HGS/VERANSTALTUNGEN/reg_form/reg_form.php?id=77

#### Mixed-Integer Programming and Combinatorial Optimization

**Date:**
2013-02-11 - 9:15

**Speaker:** Prof. Dr. Gerhard Reinelt

**Location:** IWR, Room 532

**ECTS-Points:** 4

This course gives an introduction to the theory and practice of mixed-integer programming and combinatorial optimization. It consists of lectures

and presentations of applications as well as

of computer practicals. Besides basic mathematical knowledge and programming skills there are no further requirements to be met by the participants. The workshop will be held as a 3-day compact course in English. It specifically addresses the members of the Graduate School \"Mathematical

and Computational Methods for the Sciences\", but is also open to interested students in computer science and mathematics.

http://comopt.ifi.uni-heidelberg.de/teaching/ws12/index.html

#### Convergent Adaptive Finite Element Methods:proof techniques, implementation and numerical results

**Date:**
2013-02-11 - 10:00

**Speaker:** Dr. Natasha Sharma

**Location:** Im Neuenheimer Feld 368, Room 248

**ECTS-Points:** 2

Mathematically, singularities are points in the domain of computation where the solution seems to `blow up‘ e.g. singularities arising from sharp corners. Numerical solutions are often marred by the presence of such singularities which impact its overall accuracy. To overcome this difficulty, it is natural to increase the number of grid points in certain critical regions so that the computed solution is better resolved. The task then, is to efficiently choose such critical regions and to find a balance between refined regions and unrefined regions which would yield an optimal accuracy.

Another issue faced in practical problems arising in physics and engineering, is that little information is known a priori about the computed solution. This necessitates the derivation of reliable estimates(depending only on the data of the problem) for measuring the overall accuracy of such computed solutions.

Adaptive mesh refinement is a fundamental tool in addressing the above issues and this course introduces the adaptive method for the Galerkin approximation to partial differential equations.

The adaptive method algorithm consists of the steps SOLVE, ESTIMATE, MARK and REFINE and we will discuss each of these steps with a focus on the derivation of an estimator which serves as a reliable estimate for the Galerkin approximation. The convergence of the adaptive cycle will be presented and an emphasis will be placed on discussing the techniques used in proving the convergence of this algorithm for both the continuous and discontinuous Galerkin approximations. Numerical results and examples will also be presented. This lecture series will be based on the theory developed over the past decade.

Please register here and enclose your field of study (comment):

http://hgs.iwr.uni-heidelberg.de/Portfolio_HGS/VERANSTALTUNGEN/reg_form/reg_form.php?id=82

**Key Competences**

#### Rhetorik und Kommunikation in Wissenschaft und Wirtschaft (inkl. Praxistag) []

**Date:**
2012-10-25 - 10:00

**Speaker:** Michael Müller, Maximilian Scheidt

**Location:** INF 368, Room 520

**ECTS-Points:** 1

Das Training bietet die Möglichkeit die einzelnen Bausteine eines Assessment Centers zu durchlaufen. Die Teilnehmer trainieren Selbstpräsentation, Gruppendiskussion, Rollenspiele, Postkorbübung sowie Logiktests aus Gruppenauswahlverfahren. Sie bekommen eine dezidierte Auswertung ihrer Selbstpräsentation und des Rollenspiels per Videoanalyse Darüber hinaus erhalten die Teilnehmer Informationen zu den Erwartungen der Personalverantwortlichen.

Besonderen Wert wird auf den Part des Auftretens und der Rhetorik gelegt. Den Teilnehmern wird ein besseres Gefühl für bewusstes Einsetzen von Körper und Sprache vermittelt.

In einem separaten Gespräch erhält jeder Teilnehmer ein ausführliches, individuelles Feedback, um sich weiter verbessern zu können.

Please register here:

**Lecture**

#### Modellierung und Optimierung in Robotik und Biomechanik

**Date:**
2012-10-16 - 11:00

**Speaker:** Prof. Dr. Katja Mombaur

**ECTS-Points:** 6

Acquire basic knowledge in modeling of mechanical systems, in particular in robotics (industrial, legged and humanoid robots) and biomechanics (human motion modeling); learn about simulation and optimal control tools to study human and robot motion: essential theory and lots of practical exercises to implement example problems. Particular focus on walking and running motions.

- Mechanical modeling, kinematics and dynamics

- Robotics basics

- Biomechanical modeling

- Walking and running models

- Stability

- Simulation of motions

- Optimal control of motions

- Numerical direct optimal control methods

**Public Talk**

#### Dataflow Computing for Scientific Applications

**Date:**
2012-10-18 - 16:00

**Speaker:** Dr. Vitali Averbukh and Dr. Oscar Mencer

**Location:** IWR, Im Neuenheimer Feld 368, 4th Floor Room 432

**ECTS-Points:** tbd

Since the introduction of computers into routine scientific work in the middle of the last century,

their role in the scientific endeavour has changed dramatically from mere auxiliary tools of

numerical computation into an essential element of scientific discovery. The progress in computer

technology has been leading the tremendous advances in the application of numerical techniques in

science. The available computational power and computer memory resources define the scope of

the scientific problems that can be presently addressed, as well as the achievable accuracy level of

theoretical modeling and thus also the reliability of the scientific prediction. Modern science strives

to address more and more challenging problems on a larger and larger scale using accurate

theoretical models. The present scientific objectives of computational quantum chemistry, for

example, include the study of electronic structure of molecular systems relevant to biological and

energy production processes using not only the density functional theory (DFT) techniques, but

also at the more demanding first-principles, or ab initio level. Achieving such challenging goals in

the coming years will require development of principally new powerful computational

technology. Dataflow computing is a new, very promising approach to scientific computation that

has already been proved extremely efficient for a wide range of applications both in academic

science and in the industry. Based on the more than decade-long scientific and technological

development at Stanford, Bell Labs and Imperial College London, dataflow computing equipment

is being now produced on the industrial scale by Maxeler Technologies (London, Palo Alto) and is

provided to academic users through the Maxeler University Programme. Dataflow computers show

acceleration rates of the order of 20x-40x, within the same space and power constraints, for such

diverse applications as Monte Carlo simulations, numerical solutions of ordinary and partial

differential equations, numerical integration methods, finite difference and finite elements methods,

operations with sparce matrices, and have a strong potential to do still better in future. Moreover,

when deployed on the industrial scale, dataflow computing model has led to orders-of-magnitude

lower power consumption and dramatically lower data centre space requirements. The key reason

for the success of the dataflow model is the “vertical” multidisciplinary approach to scientific

computation whereby instead of optimizing algorithms to standard microprocessors, the dataflow

computer is designed to match the given computational problem. This presentation will discuss the

general principle and the implementation details of dataflow computer operation and give an

overview of the applications of dataflow technology. We shall also present the unique user-friendly

dataflow programming environment that makes the exciting opportunities of the dataflow systems

available to the wide community of researchers interested in scientific computing.

#### Weltbilder der Informatik []

**Date:**
2012-10-24 - 19:15

**Speaker:** Prof. Dr. Britta Schinzel

**Location:** Mathematisches Institut HS2

**ECTS-Points:** tbd

In diesem Vortrag werden Absichten und Ergebnisse unseres zweiteiligen DFG-Projekts „Weltbilder der Informatik“ vorgestellt und im Anschluss notwendige Schlussfolgerungen für Unterricht und Studium der Informatik diskutiert.

Das Projekt ging davon aus, dass Weltbilder nicht nur die Ziele der Informatik, sowie die soziale Situation in Studium und Informatikberufen beeinflussen, sondern auch die Art, Nutzbarkeit und Qualität ihrer Produkte.

Im ersten Teil des o.g. Projekts wurden die Weltbilder der Informatikstudierenden hinsichtlich der sieben Schwerpunkte: Technikbild, Wirklichkeitsauffassung, Relation Realität – informatische Rekonstruktion derselben, Menschenbild, Relation Mensch-Maschine, Relation EntwicklerInnen – NutzerInnen, sowie Berufsbild Informatik untersucht. Herausragende Ergebnisse waren dabei u.a. die mangelnde Diversität im Studium der Informatik, sowohl personell als auch hinsichtlich der Inhalte, Foci und Lehrmethoden und ihre Ursachen, die durchs Studium beeinflusste Verantwortungsfrage und das Geschlechterwissen der Studierenden.

In einer folgenden Analyse wurden die gewonnenen Daten ein zweites mal hinsichtlich der Fragestellungen: Bild der Informatik in der Öffentlichkeit, Eigenbild der Informatik und die Situation der Studierenden ausgewertet. Die Ergebnisse können als empirische Basis für die aktuelle Diskussion in den Berufsverbänden und für eine Aktualisierung der Curricula dienen.

#### Locomotion of Multibody Systems: Dynamics and Optimization

**Date:**
2012-11-30 - 16:15

**Speaker:** Prof. Felix L. Chernousko

**Location:** IWR, Im Neuenheimer Feld 368, 4th Floor Room 432

**ECTS-Points:** tbd

Several principles of locomotion for multibody mechanical systems are discussed. Locomotion is based on the change of the system configuration and is possible in the presence of the resistive medium. Snake-like multilink systems, fish-like and frog-like systems, and also systems containing internal moving masses are considered. Various resistance forces including linear and quadratic forces depending on the velocity as well as dry friction forces, both isotropic and anisotropic, are taken into account. Dynamics and control of locomotion are analyzed. Optimal values of the system parameters as well as optimal controls are found that correspond to the maximal speed of locomotion. Experimental results are presented, and possible applications to robotic systems, especially to mini-robots, are discussed. The talk is based on the results obtained in the Institute for Problems in Mechanics of the Rus-sian Academy of Sciences.

#### Von Dunkler Materie bis Alpha Centauri

**Date:**
2013-03-04 - 18:00

**Speaker:** Prof. Dr. Harald Lesch

**Location:** Hörsaal 1, INF 306

**ECTS-Points:** tbd

**Abstract - File:** []

**School**

#### Summer School: Subsurface transport of water and solutes

**Date:**
2012-09-24 - 9:00

**Speaker:** Dr. Olaf Ippisch, Prof. Dr. Kurt Roth, H.J. Vogel

**Location:** IWR INF 368 R 432 and OMZ U011/U012

**ECTS-Points:** 3

The students

- have understood thorougly the transport processes in natural terrestrical systems

- know the limits of the classical methods

- can efficently use modern numerical simulation tools

Fundamental physical processes and current concepts for subsurface transport of water and solutes

- multiscale aspects of sedimentary material

- macroscopic phenomena and effective descriptions

- numerical simulation of flow and transport in porous media

Prerequisites: Basic knowledge of terrestrial sysgtems recommended

**Seminar**

#### Methods for Differentiation in Optimization

**Date:**
2012-01-01 - 16:00

**Speaker:** Prof. Bock, Andreas Schmidt

**Location:** OMZ

**ECTS-Points:** not yet determined

Numerical methods for the solution of finite dimensional optimization problems often need the computation of derivatives.

The function to be derived might be complicated, e.g. it can contain the solution of a ordinary or partial differential equation. In the seminar we will get to know methods to compute these derivatives. One efficient technique is automatic differentiation, which will be the main focus.

#### Direct Methods for Sparse Linear Systems

**Date:**
2012-10-17 - 14:00

**Speaker:** Prof. Dr. Dr. h. c. Hans Georg Bock, Dr. Andreas Potschka

**Location:** IWR, room 532

**ECTS-Points:** 4

Sparse linear systems of the form A x = b feature only few entries in each row of A. All other entries are zero. Often, these systems are large, with 10,000 to 100,000 rows and columns. Matrices of this type stem from various applications, e.g., the discretization of partial differential equations. In this seminar, we study algorithms that decompose A into easy to solve factors while ensuring sparsity of those factors. These methods can sometimes constitute a convenient alternative to iterative solution methods (compare current course by Mario Mommer).

#### Methods for Differentiation in Optimization

**Date:**
2012-10-18 - 16:00

**Speaker:** Prof. Dr. Dr. h. c. Hans Georg Bock, Andreas Schmidt

**Location:** OMZ, INF 350, Raum U013

**ECTS-Points:** 4

Numerical methods for the solution of finite dimensional optimization problems often need the computation of derivatives.

The function to be derived might be complicated, e.g. it can contain the solution of a ordinary or partial differential equation. In the seminar we will get to know methods to compute these derivatives. One efficient technique is automatic differentiation, which will be the main focus.

**Software Training**

#### Robotics programming and hardware project

**Date:**
2012-10-19 - 13:00

**Speaker:** Prof. Dr. Katja Mombaur, Thomas Kloepfer

**Location:** OMZ,INF 350, Robotics Lab

**ECTS-Points:** 8

- Individual robotics projects on different topics.

- All topics will be presented during preliminary discussion.

Participants will practices to program different robots to do cool stuff. The course improves programming skills, learn about micro controllers, mechanics, design, control etc.

**Talk**

#### Optimizing Counter-Terror Operations

**Date:**
2012-11-14 - 10:00

**Speaker:** Prof. Dr. Gustav Feichtinger

**Location:** IWR, INF 368, r 432

**ECTS-Points:** tbd

Considering the aftermaths of September 11th, it is needless to say that the impact of terror and counter-terror measures poses many complex challenges to decision makers such as governments, security and military organizations. The purpose of the present contribution is to illustrate how methods of optimal control and dynamic games may be applied to

terror related problems to provide insights into questions of how to effectively fight terror. The state variable of such an intertemporal conflict situation, x, corresponds to the number of terrorists (or,

more generally, the power of this organization). In the resulting two-player differential game both opponents have to select the intensity of attacks and counter-attacks both reducing the strength x. Both

opponents have to take into consideration the trade-off between the utility and the costs of their measures. Two versions of a one-state non-zero sum dynamic game are presented. In the first case the terrorists are interested both in becoming powerful (by increasing x) as well as maximizing their attacks, while the target country intends to eliminate as many terrorists as possible. Focusing

our analysis to open-loop Nash equilibria, we are able to derive a stable limit cycle for the long-run behavior. Note that the government´s efforts follow essentially the periodic strength of the terrorists,

whereas the terrorists behave anti-cyclically.

In another version, the target country tries to minimize the strength of the terrorists as well as the intensity of their attacks, while the terrorists_ political objectives induce excessive counter-attacks as an

indirect way of stirring up sentiments against the target country. Moreover, the systems dynamics includes the (undesirable indirect) effect in increasing the recruitment rate of terrorists due to collateral damages induced by the target country´s counter-terror measures. Confining to the interior solutions, we are able to calculate stationary Nash equilibria. Due to the state-separability of this dynamic game, its open-loop Nash equilibrium qualifies as Markovian (feedback) solution. The state-control separability allows to determine also stationary Stackelberg solutions. The explicit calculations allow a comparative static analysis delivering valuable insights into the design of optimal counter-terror strategies.

#### Evidence synthesis for estimating burden of infectious diseases []

**Date:**
2012-11-20 - 14:15

**Speaker:** Dr. Anne Presanis

**Location:** BIOQUANT, room 042

**ECTS-Points:** tbd

Estimation of key characteristics of infectious disease, such as prevalence, incidence or severity, is challenging, as these quantities are typically not easy to measure directly. However, they may be estimated potentially from a network of information from multiple and varied sources, combining these data using evidence synthesis methods. The available data sources relevant to the disease under study may include, for example, surveillance systems, observational studies, registries and community surveys. Such data may be incomplete and/or biased, therefore only indirectly informing the quantities to be estimated. To synthesise such diverse and challenging data usually implies the formulation of complex probabilistic models, often in a Bayesian framework. In the context of such complexity, critical model assessment, including the detection of conflicting evidence, is essential. We illustrate these concepts through examples such as the estimation of HIV prevalence and modelling influenza severity.

#### Dynamical properties of billiards and flows on surfaces []

**Date:**
2012-11-22 - 17:00

**Speaker:** Dr. Corinna Ulcigrai

**Location:** INF 288, HS 2

**ECTS-Points:** tbd

In a mathematical billiard a particle moves without friction in a planar domain bouncing elastically at the boundary. Billiards inside rational polygons and area preserving flows on surfaces are two examples of dynamical systems which can be studied using Teichmueller dynamics, a topical and exciting fields of research. We will give a brief introduction to the study of mathematical billiards and present some recent results on billiards in regular polygons (joint work with J. Smillie) and chaotic properties of area preserving flows on surfaces.

#### Asymptotically correct discontinuous Galerkin methods for radiative transfer problems

**Date:**
2012-11-30 - 14:15

**Speaker:** Prof. Guido Kanschat

**Location:** 14:15, IWR room 432

**ECTS-Points:** tbd

While discontinuous Galerkin (DG) methods had been developed and analyzed in the 1970s and 80s

with applications in radiative transfer and neutron transport in mind, it was pointed out later in the

nuclear engineering community, that the upwind DG discretization by Reed and Hill may fail to produce

physically relevant approximations, if the scattering mean free path length is smaller than the mesh size. Mathematical analysis reveals, that in this case, convergence is only achieved in a continuous subspace of the finite element space. Furthermore, if boundary conditions are not chosen isotropically, convergence can only be expected in relatively weak topology. While the latter result is a property of the transport model, asymptotic analysis reveals, that the forcing into a continuous subspace can be avoided. By choosing a weighted upwinding, the conditions on the diffusion limit can be weakened. It has been known for long time, that the so called diffusion limit of radiative transfer is the solution to a diffusion equation; it turns out, that by choosing the stabilization carefully, the DG method can yield either the LDG method or the method by Ern and

Guermond in its diffusion limit. Finally, we will discuss an efficient and robust multigrid method for the resulting discrete problems.

#### The model of closed-loop control by thermostats: applications, properties and optimization.

**Date:**
2012-12-04 - 14:15

**Speaker:** Grzegorz Dudziuk

**Location:** Institute of Mathematics, room 214, INF 294

**ECTS-Points:** tbd

#### Mathematical and Computational Modelling of Tissue Engineered Bone in a Hydrostatic Bioreactor

**Date:**
2013-01-15 - 15:15

**Speaker:** Katie Leonard

**Location:** BIOQUANT SR 043.

**ECTS-Points:** tbd

The use of tissue engineered implants could facilitate unions in situations where there is loss of bone or non-union, thereby increasing healing time, reducing the risk of infections and hence reducing morbidity. Currently engineered bone tissue is not of sufficient quality to be used in widespread clinical practice. In order to improve experimental design, and thereby the quality of the tissue-constructs, the underlying biological processes involved need to be better understood.

In conjunction with experimentalists, we consider the effect hydrodynamic pressure has on the development and regulation of bone, in a bioreactor designed specifically for this purpose.

To answer the experimentalists’ specific questions, we have developed a time-dependent mathematical model describing the development of the bone-producing cells and mineralised collagen. Two separate hypothesis of the mineralised extracellular matrix deposition rate are considered.

In order to represent experimental results, it is demonstrated that in incluing a decay rate to account for length of loading above a pressure threshold is needed. The mathematical model is then used to computationally screen for operating parameters in order to determine the optimal experimental strategy.

#### Eolian 2: Universidad de Chile`s Solar Car

**Date:**
2013-02-07 - 11:15

**Speaker:** Enrique Guerrero M.

**Location:** IWR, room 432

**ECTS-Points:** tbd

Solar car races are events that take place regularly in different

countries (Australia, Chile, Japan, South Africa, United States), posing

the challenge to cross long distances in vehicles powered only by solar

energy, raising thus very interesting optimization problems with

perturbations, stochasticity, nonlinearities and unknown parameters. The

talk will explain basic concepts about solar cars, solar car races and

the problems that arise, giving special emphasis in the cooperation

windows that could exist in which the IWR tools or others could be

applied.

**Workshop**

#### Workshop on Discrete Graphical Models and Combinatorial Optimization []

**Date:**
2012-11-08 - 13:00

**Speaker:** Dr. Jörg Kappes

**Location:** HCI, Speyerer Straße 6, 69115 Heidelberg

**ECTS-Points:** 1

#### Numerical simulations of Fluid Structure Interaction problems via Immersed Methods: a variational implementation

**Date:**
2013-03-07 - 14:15

**Speaker:** Prof. Luca Heltai

**Location:** INF 368, Room 432

**ECTS-Points:** not yet determined

Several methods exist in the literature that allow the numerical treatment of FSI problems via two independent grids, one Eulerian, where the independent variable (x) denotes a fixed point in space, and one Lagrangian, \"immersed\" in the first grid, where the independent variable (s) denotes a material particle in a reference domain. The coupling between the two grids can be achieved in several ways, depending on the underlying discretisation techniques.

The original method was first introduced by Peskin (Immersed Boundary Method - IBM) in the late seventies, to simulate the interaction between blood flow and heart valves. In that method, the coupling is obtain via approximations of Dirac-delta distributions, which allowed a clever interpolation between a finite difference grid and a collection of fibers, used to simulate the immersed body. Another type of Dirac-delta approximation (Reproducing Kernel Particle Method - RKPM) was used instead in the first formulation of the Immersed Finite Element Method (IFEM).

By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This was shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level.

In this talk, I will present a generalisation of the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems.

In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non-matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, I will focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.