Habib Ammari: Catalogue data in Spring Semester 2017 |
| Name | Prof. Dr. Habib Ammari |
| Field | Applied Mathematics |
| Address | Seminar für Angewandte Mathematik ETH Zürich, HG G 57.3 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 633 80 31 |
| habib.ammari@sam.math.ethz.ch | |
| URL | http://www.sam.math.ethz.ch/~hammari |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-2654-00L | Numerical Analysis II | 6 credits | 3V + 2U | H. Ammari | |
| Abstract | The central topic of this course is the numerical treatment of ordinary differential equations. It focuses on the derivation, analysis, efficient implementation, and practical application of single step methods and pay particular attention to structure preservation. | ||||
| Learning objective | The course aims to impart knowledge about important numerical methods for the solution of ordinary differential equations. This includes familiarity with their main ideas, awareness of their advantages and limitations, and techniques for investigating stability and convergence. Further, students should know about structural properties of ordinary diferential equations and how to use them as guideline for the selection of numerical integration schemes. They should also acquire the skills to implement numerical integrators in MATLAB and test them in numerical experiments. | ||||
| Content | 1 Einleitung 1.1 Anfangswertprobleme (AWP) 1.2 Beispiele und Grundbegriffe 1.2.1 Okologie 1.2.2 Chemische Reaktionskinetik 1.2.3 Physiologie 1.2.4 Mechanik 1.3 Theorie 1.3.1 Existenz und Eindeutigkeit von Loesungen 1.3.2 Lineare AWPe 1.3.3 Sensitivitaet 1.3.3.1 Grundbegriffe 1.3.3.2 Unser Problem: das Anfangswertproblem 1.3.3.3 Wohlgestelltheit 1.3.3.4 Asymptotische Kondition 1.3.3.5 Schlecht konditionierte AWPe 1.4 Polygonzugverfahren 1.4.1 Das explizite Euler-Verfahren 1.4.2 Das implizite Euler-Verfahren 1.4.3 Implizite Mittelpunktsregel 1.4.4 Stoermer-Verlet-Verfahren 2 Einschrittverfahren 2.1 Grundlagen 2.1.1 Abstrakte Einschrittverfahren 2.1.2 Konsistenz 2.1.3 Konvergenz 2.1.4 Das Aequivalenzprinzip 2.1.5 Reversibilitaet 2.2 Kollokationsverfahren 2.2.1 Konstruktion 2.2.2 Konvergenz von Kollokationsverfahren 2.3 Runge-Kutta-Verfahren 2.3.1 Konstruktion 2.3.2 Konvergenz 2.4 Extrapolationsverfahren 2.4.1 Der Kombinationstrick 2.4.2 Extrapolationsidee 2.4.3 Extrapolation von Einschrittverfahren 2.4.4 Lokale Extrapolations-Einschrittverfahren 2.4.5 Ordnungssteuerung 2.4.6 Extrapolation reversibler Einschrittverfahren 2.5 Splittingverfahren 2.6 Schrittweitensteuerung 3 Stabilitaet 3.1 Modellproblemanalyse 3.2 Vererbung asymptotischer Stabilitaet 3.3 Nichtexpansivitaet 3.4 Gleichmaessige Stabilitaet 3.5 Steifheit 3.6 Linear-implizite Runge-Kutta-Verfahren 3.7 Exponentielle Integratoren 3.8 Differentiell-Algebraische Anfangswertprobleme 3.8.1 Grundbegriffe 3.8.2 Runge-Kutta-Verfahren fuer Index-1-DAEs 3.8.3 DAEs mit hoeherem Index 4 Strukturerhaltende numerische Integration 4.1 Polynomiale Invarianten 4.2 Volumenerhaltung 4.3 Verallgemeinerte Reversibilitaet 4.4 Symplektizitaet 4.4.1 Symplektische Evolutionen Hamiltonscher Differentialgleichungen 4.4.2 Symplektische Integratoren 4.4.3 Rueckwaertsanalyse 4.4.4 Modifizierte Gleichungen: Fehleranalyse 4.4.5 Strukturerhaltende modifizierte Gleichungen 4.5 Methoden fuer oszillatorische Differentialgleichungen | ||||
| Lecture notes | Lecture slides including supplements will be provided electronically. Please find the lecture homepage here: http://www.sam.math.ethz.ch/~grsam/FS17/NAII/index.html All assignments and some previous lecture notes will be available for download on lecture homepage. | ||||
| Literature | Note: Extra reading is not considered important for understanding the course subjects. Deuflhard and Bornemann: Numerische Mathematik II - Integration gewöhnlicher Differentialgleichungen, Walter de Gruyter & Co., 1994. Hairer and Wanner: Solving ordinary differential equations II - Stiff and differential-algebraic problems, Springer-Verlag, 1996. Hairer, Lubich and Wanner: Geometric numerical integration - Structure-preserving algorithms for ordinary differential equations}, Springer-Verlag, Berlin, 2002. L. Gruene, O. Junge "Gewoehnliche Differentialgleichungen", Vieweg+Teubner, 2009. Hairer, Norsett and Wanner: Solving ordinary differential equations I - Nonstiff problems, Springer-Verlag, Berlin, 1993. Walter: Gewöhnliche Differentialgleichungen - Eine Einführung, Springer-Verlag, Berlin, 1972. Walter: Ordinary differential equations, Springer-Verlag, New York, 1998. | ||||
| Prerequisites / Notice | Homework problems involve MATLAB implementation of numerical algorithms. | ||||
| 401-3920-17L | Numerical Analysis Seminar: Mathematics for Biomimetics  Number of participants limited to 8. | 4 credits | 2S | H. Ammari | |
| Abstract | The aim of this seminar is to explore how we can learn from Nature to provide new approaches to solving some of the most challenging problems in sensing systems and materials science. An emphasis will be put on the mathematical foundation of bio-inspired pressure and temperature sensing membranes and shape perception algorithms in electrolocation and echolocation. | ||||
| Learning objective | |||||
| 401-4788-16L | Mathematics of (Super-Resolution) Biomedical Imaging | 8 credits | 4G | H. Ammari | |
| Abstract | The aim of this course is to review different methods used to address challenging problems in biomedical imaging. The emphasis will be on scale separation techniques, hybrid imaging, spectroscopic techniques, and nanoparticle imaging. These approaches allow one to overcome the ill-posedness character of imaging reconstruction in biomedical applications and to achieve super-resolution imaging. | ||||
| Learning objective | Super-resolution imaging is a collective name for a number of emerging techniques that achieve resolution below the conventional resolution limit, defined as the minimum distance that two point-source objects have to be in order to distinguish the two sources from each other. In this course we describe recent advances in scale separation techniques, spectroscopic approaches, multi-wave imaging, and nanoparticle imaging. The objective is fivefold: (i) To provide asymptotic expansions for both internal and boundary perturbations that are due to the presence of small anomalies; (ii) To apply those asymptotic formulas for the purpose of identifying the material parameters and certain geometric features of the anomalies; (iii) To design efficient inversion algorithms in multi-wave modalities; (iv) to develop inversion techniques using multi-frequency measurements; (v) to develop a mathematical and numerical framework for nanoparticle imaging. In this course we shall consider both analytical and computational matters in biomedical imaging. The issues we consider lead to the investigation of fundamental problems in various branches of mathematics. These include asymptotic analysis, inverse problems, mathematical imaging, optimal control, stochastic modelling, and analysis of physical phenomena. On the other hand, deriving mathematical foundations, and new and efficient computational frameworks and tools in biomedical imaging, requires a deep understanding of the different scales in the physical models, an accurate mathematical modelling of the imaging techniques, and fine analysis of complex physical phenomena. An emphasis is put on mathematically analyzing acoustic-electric imaging, thermo-elastic imaging, Lorentz force based imaging, elastography, multifrequency electrical impedance tomography, and plasmonic resonant nanoparticles. | ||||
| 401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics  | 0 credits | 2K | R. Abgrall, R. Alaifari, H. Ammari, U. S. Fjordholm, A. Jentzen, S. Mishra, S. Sauter, C. Schwab | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||