Ralf Hiptmair: Catalogue data in Spring Semester 2023 |
| Name | Prof. Dr. Ralf Hiptmair |
| Field | Mathematik |
| Address | Seminar für Angewandte Mathematik ETH Zürich, HG G 58.2 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 34 04 |
| Fax | +41 44 632 11 04 |
| ralf.hiptmair@sam.math.ethz.ch | |
| URL | https://www.math.ethz.ch/sam/the-institute/people/ralf-hiptmair.html |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||||||||||||||||||||
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| 401-0674-AAL | Numerical Methods for Partial Differential Equations Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 10 credits | 21R | R. Hiptmair | |||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations,among them (convection)-diffusion and heat equations, wave equation, conservation laws. Implementation in C++ based on a finite element library. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Main skills to be acquired in this course: * Ability to implement fundamental numerical methods for the solution of partial differential equations efficiently. * Ability to modify and adapt numerical algorithms guided by awareness of their mathematical foundations. * Ability to select and assess numerical methods in light of the predictions of theory * Ability to identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm. * Ability to understand research publications on theoretical and practical aspects of numerical methods for partial differential equations. * Skills in the efficient implementation of finite element methods on unstructured meshes. This course is neither a course on the mathematical foundations and numerical analysis of methods nor an course that merely teaches recipes and how to apply software packages. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | See the contents of 401-0674-00 Numerical Methods for Partial Differential Equations | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | The lecture will be taught in flipped classroom format: - Video tutorials for all thematic units will be published online. - Tablet notes accompanying the videos will be made available to the audience as PDF. - A comprehensive PDF handout will cover all aspects of the lecture. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | See the information given for 401-0674-00 Numerical Methods for Partial Differential Equations | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Mastery of basic calculus and linear algebra is taken for granted. Familiarity with fundamental numerical methods (solution methods for linear systems of equations, interpolation, approximation, numerical quadrature, numerical integration of ODEs) is essential. Important: Coding skills and experience in C++ are essential. Homework assignments involve substantial coding, partly based on a C++ finite element library. The written examination will be computer based and will comprise coding tasks. | ||||||||||||||||||||||||||||||||||||||||||||||||||
Competencies |
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| 401-0674-00L | Numerical Methods for Partial Differential Equations Not meant for BSc/MSc students of mathematics. | 10 credits | 2G + 2U + 2P + 4A | R. Hiptmair | |||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations: convection-diffusion, heat equation, wave equation, conservation laws. Implementation in C++ based on a finite element library. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Main skills to be acquired in this course: * Ability to implement fundamental numerical methods for the solution of partial differential equations efficiently. * Ability to modify and adapt numerical algorithms guided by awareness of their mathematical foundations. * Ability to select and assess numerical methods in light of the predictions of theory * Ability to identify features of a PDE (= partial differential equation) based model that are relevant for the selection and performance of a numerical algorithm. * Ability to understand research publications on theoretical and practical aspects of numerical methods for partial differential equations. * Skills in the efficient implementation of finite element methods on unstructured meshes. This course is neither a course on the mathematical foundations and numerical analysis of methods nor an course that merely teaches recipes and how to apply software packages. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Second-order scalar elliptic boundary value problems Finite-element methods (FEM) FEM: Convergence and Accuracy Non-linear elliptic boundary value problems Second-order linear evolution problems Convection-diffusion problems Numerical methods for conservation laws | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | The lecture will be taught in flipped classroom format: - Video tutorials for all thematic units will be published online. - Tablet notes accompanying the videos will be made available to the audience as PDF. - A comprehensive lecture document will cover all aspects of the course, see https://www.sam.math.ethz.ch/~grsam/NUMPDEFL/NUMPDE.pdf | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Chapters of the following books provide supplementary reading (detailed references in course material): * D. Braess: Finite Elemente, Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie, Springer 2007 (available online). * S. Brenner and R. Scott. Mathematical theory of finite element methods, Springer 2008 (available online). * A. Ern and J.-L. Guermond. Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer, New York, 2004. * Ch. Großmann and H.-G. Roos: Numerical Treatment of Partial Differential Equations, Springer 2007. * W. Hackbusch. Elliptic Differential Equations. Theory and Numerical Treatment, volume 18 of Springer Series in Computational Mathematics. Springer, Berlin, 1992. * P. Knabner and L. Angermann. Numerical Methods for Elliptic and Parabolic Partial Differential Equations, volume 44 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * S. Larsson and V. Thomée. Partial Differential Equations with Numerical Methods, volume 45 of Texts in Applied Mathematics. Springer, Heidelberg, 2003. * R. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK, 2002. However, study of supplementary literature is not important for for following the course. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Mastery of basic calculus and linear algebra is taken for granted. Familiarity with fundamental numerical methods (solution methods for linear systems of equations, interpolation, approximation, numerical quadrature, numerical integration of ODEs) is essential. Important: Coding skills and experience in C++ are essential. Homework assignments involve substantial coding, partly based on a C++ finite element library. The written examination will be computer based and will comprise coding tasks. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Competencies |
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| 401-2673-AAL | Numerical Methods for CSE Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 9 credits | 19R | R. Hiptmair | |||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | * Knowledge of the fundamental algorithms in numerical mathematics * Knowledge of the essential terms in numerical mathematics and the techniques used for the analysis of numerical algorithms * Ability to choose the appropriate numerical method for concrete problems * Ability to interpret numerical results * Ability to implement numerical algorithms afficiently in C++ | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | 1. Computing with Matrices and Vectors 2. Direct Methods for Linear Systems of Equations 3. Direct Methods for Linear Least Squares Problems 4. Filtering Algorithms 5. Data Interpolation and Data Fitting in 1D 6. Approximation of Functions in 1D 7. Numerical Quadrature 8. Iterative Methods for Non-linear Systems of Equations 12. Numerical Integration - Single Step Methods 13. Single Step Methods for Stiff Initial Value Problems | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | https://people.math.ethz.ch/~grsam/HS16/NumCSE/NumCSE16.pdf | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006. M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002 P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002 U. Ascher and C. Greif "A first course in Numerical Methods" | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Examination will be conducted at the computer and will involve coding in C++/Eigen. A course covering the material is taught in English every autumn term (course unit 401-0663-00L). Course documents, exercises and examinations are available online. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 401-3650-72L | Rational Approximation and Interpolation  | 4 credits | 2S | R. Hiptmair | |||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | The seminar covers theory and algorithms for rational interpolation based on classical and modern literature. The various topics have to be presented by groups of students. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Participants of the seminar should acquire familiarity with the theoretical properties of approximation by means of rational functions as well as knowledge about algorithms used for computing approximating or interpolating rational functions. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | The simplest and most widely used function system for approximation in computational mathematics are polynomials. They are ideally suited for smooth (analytic) functions. However, in many application we encounter functions with kinks and other kinds of singularities. In this case approximation by rational functions, that is, quotients of polynomials, may be vastly superior. This is why rational approximation and interpolation is receiving increased attention for the construction of surrogate models in model order reduction. This seminar will study a number of research papers dealing with both theoretical and algorithmic aspects of rational approximation and interpolation. Topics: 1. Best approximation by rational functions 2. Best rational approximation of x 7→ |x| 3. Meinardus conjecture 4. Approximation by composite rational functions 5. Rational interpolation and linearized least-squares 6. Padé approximationj 7. Vector fitting 8. The AAA algorithm for rational approximation 9. The RKFIT algorithm for non-linear rational approximation 10. Rational minimax approximation 11. Multivariate Padé approximation 12. Fast least-squares Padé approximation Student groups will be decided and topics will be assigned during the preparatory meeting on March 1, 2023 Implementation and numerical experiments: Quite a few of the topics are algorithmic in nature. Many of the related papers mention open source implementations of the methods, mainly in MATLAB, often relying on the Chebfun library. It is desirable that groups presenting an algorithmic topic also conduct numerical experiments, those covered in the articles or others, and report their observations. More information: https://people.math.ethz.ch/~ralfh/Seminars/RAP_23/SeminarRAP_FS23.pdf | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | See https://people.math.ethz.ch/~ralfh/Seminars/RAP_23/SeminarRAP_FS23.pdf | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Good skills in analysis are required as well as basic familiarity with numerical methods for interpolation and approximation with polynomials. Preparatory meeting onj Wed March 1 Every presentation has to be done jointly by a group of 2-3 students with presenters selected at random. Every participant will have to present on 2-3 occasions. See https://people.math.ethz.ch/~hiptmair/Seminars/RAP_23/SeminarRAP_FS23.pdf for more information. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Competencies |
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| 401-3667-23L | Case Studies Seminar (Spring Semester 2023) | 3 credits | 2S | V. C. Gradinaru, R. Hiptmair, R. Käppeli, M. Reiher | |||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | In the CSE Case Studies Seminar invited speakers from ETH, from other universities as well as from industry give a talk on an applied topic. Beside of attending the scientific talks students are asked to give short presentations (10 minutes) on a published paper out of a list. | ||||||||||||||||||||||||||||||||||||||||||||||||||
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| Content | In the CSE Case Studies Seminar invited speakers from ETH, from other universities as well as from industry give a talk on an applied topic. Beside of attending the scientific talks students are asked to give short presentations (10 minutes) on a published paper out of a list (containing articles from, e.g., Nature, Science, Scientific American, etc.). If the underlying paper comprises more than 15 pages, two or three consecutive case studies presentations delivered by different students can be based on it. Consistency in layout, style, and contents of those presentations is expected. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | The talks ar in presence only (no zoom)! Student talks are in parallel sessions in the two rooms, the invited talks take place in the larger lecture hall. 75% attendance and a short presentation on a published paper out of a list or on some own project are mandatory. Students have to register their presentations online until the second Wednesday of the semester on https://rw.ethz.ch/the-programme/case-studies.html The student talks will be grouped by subject, so we'll decide the actual dates of the individual talks. Students that realize that they will not fulfill this criteria have to contact the teaching staff or de-register before the end of semester from the Seminar if they want to avoid a "Fail" in their documents. Later de-registrations will not be considered. | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Competencies |
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| 401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics | 0 credits | 1K | R. Abgrall, R. Alaifari, H. Ammari, R. Hiptmair, S. Mishra, S. Sauter, C. Schwab | |||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Research colloquium | ||||||||||||||||||||||||||||||||||||||||||||||||||
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