Peter Arbenz: Catalogue data in Autumn Semester 2012 |
Name | Prof. em. Peter Arbenz |
arbenz@inf.ethz.ch | |
URL | http://www.inf.ethz.ch/personal/arbenz/ |
Department | Computer Science |
Relationship | Retired Adjunct Professor |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
252-5251-00L | Computational Science | 2 credits | 2S | P. Arbenz, T. Hoefler, P. Koumoutsakos | |
Abstract | Class participants study and make a 40 minute presentation (in English) on fundamental papers of Computational Science. A preliminary discussion of the talk (structure, content, methodology) with the responsible professor is required. The talk has to be given in a way that the other seminar participants can understand it and learn from it. Participation throughout the semester is mandatory. | ||||
Objective | Studying and presenting fundamental works of Computational Science. Learning how to make a scientific presentation. | ||||
Content | Class participants study and make a 40 minute presentation (in English) on fundamental papers of Computational Science. A preliminary discussion of the talk (structure, content, methodology) with the responsible professor is required. The talk has to be given in a way that the other seminar participants can understand it and learn from it. Participation throughout the semester is mandatory. | ||||
Lecture notes | none | ||||
Literature | Papers will be distributed in the first seminar in the first week of the semester | ||||
263-5001-00L | Introduction to Finite Elements and Sparse Linear System Solving | 4 credits | 2V + 1U | P. Arbenz | |
Abstract | The finite element (FE) method is the method of choice for (approximately) solving partial differential equations on complicated domains. In the first third of the lecture, we give an introduction to the method. The rest of the lecture will be devoted to methods for solving the large sparse linear systems of equation that a typical for the FE method. We will consider direct and iterative methods. | ||||
Objective | Students will know the most important direct and iterative solvers for sparse linear systems. They will be able to determine which solver to choose in particular situations. | ||||
Content | I. THE FINITE ELEMENT METHOD (1) Introduction, model problems. (2) Variational formulations. (3) Galerkin finite element method. (4) Implementation aspects. II. DIRECT SOLUTION METHODS (5) LU and Cholesky decomposition. (6) Sparse matrices. (7) Fill-reducing orderings. III. ITERATIVE SOLUTION METHODS (8) Stationary iterative methods, preconditioning. (9) Preconditioned conjugate gradient method (PCG). (10) Incomplete factorization preconditioning. (11) Multigrid preconditioning. (12) Nonsymmetric problems (GMRES, BiCGstab). (13) Indefinite problems (SYMMLQ, MINRES). | ||||
Literature | [1] H. Elman, D. Sylvester, A. Wathen: Finite elements and fast iterative solvers. OUP, Oxford, 2005. [2] Y. Saad: Iterative methods for sparse linear systems (2nd ed.). SIAM, Philadelphia, 2003. [3] T. Davis: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia, 2006. [4] P.Knabner, L.Angermann: Numerik partieller Differentialgleichungen. Springer, Berlin, 2000. Engl. translation: Numerical methods for elliptic and parabolic partial differential equations. Springer, New York, 2003. [5] H.R. Schwarz: Die Methode der finiten Elemente (3rd ed.). Teubner, Stuttgart, 1991. | ||||
Prerequisites / Notice | Prerequisites: Linear Algebra, Analysis, Computational Science. The exercises are made with Matlab. | ||||
401-0663-00L | Numerical Methods for CSE | 7 credits | 4V + 2U | P. Arbenz | |
Abstract | The course gives an introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. The courses focuses on fundamental ideas and algorithmic aspects of numerical methods. The exercises involve actual implementation of numerical methods. | ||||
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 | ||||
Content | 1. Direct Methods for linear systems of equations 2. Interpolation 3. Iterative Methods for non-linear systems of equations 4. Krylov methods for linear systems of equations 5. Eigensolvers 6. Least Squares Techniques 7. Filtering Algorithms 8. Approximation of Functions 9. Numerical Quadrature 10. Clustering Techniques 11. Single Step Methods for ODEs 12. Stiff Integrators 13. Structure Preserving Integrators | ||||
Lecture notes | Lecture slides will be made available to participants. | ||||
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 C. Moler, Numerical computing with MATLAB, SIAM, 2004 P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002 | ||||
Prerequisites / Notice | The course will be accompanied by programming exercises relying on the high level programming language MATLAB. A brief introduction to Matlab will be given during the first week. | ||||
406-0663-AAL | Numerical Methods for CSE Enrolment only for MSc students who need this course as additional requirement. | 7 credits | 15R | P. Arbenz | |
Abstract | Introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. | ||||
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 | ||||
Content | The course will cover the following chapters: 1. Direct Methods for linear systems of equations 2. Interpolation 3. Iterative Methods for non-linear systems of equations 4. Krylov methods for linear systems of equations 5. Eigensolvers 6. Least Squares Techniques 7. Filtering Algorithms 8. Approximation of Functions 9. Numerical Quadrature 10. Clustering Techniques 11. Single Step Methods for ODEs 12. Stiff Integrators | ||||
Lecture notes | Comprehensive lecture materials are available upon request from the lecturer. | ||||
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 C. Moler, "Numerical computing with MATLAB", SIAM, 2004 P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002 | ||||
Prerequisites / Notice | Solid knowledge about fundamental concepts and technques from linear algebra & calculus as taught in the first year of science and engineering curricula. |