Carlos Jerez Hanckes: Catalogue data in Autumn Semester 2018

Name Prof. Dr. Carlos Jerez Hanckes
(Professor Pontificia Universidad Católica de Chile (PUC) - Santiago de Chile)
Address
Barbara Hermann
Rämistrasse 101, HG G 58.3
Seminar für Angewandte Mathematik
8092 Zürich
SWITZERLAND
DepartmentMathematics
RelationshipVisiting Professor

NumberTitleECTSHoursLecturers
401-4640-68LUncertainty Quantification in Electromagnetism Restricted registration - show details
Number of participants limited to 10
4 credits2SC. Jerez Hanckes
AbstractIn this seminar we will discuss, through the reading of recent papers, state-of-the-art techniques in uncertainty quantification as well as some typical numerical methods to model electromagnetic problems with uncertainty.
ObjectiveWe will understand state-of-the-art techniques in uncertainty quantification as well as some typical numerical methods to model electromagnetic problems with uncertainty.
Content1. Basics of Electromastatics and Electromagnetic
2. Basics of Finite Element and Boundary Element Methods
3. Introduction of different UQ techniques
4. Application of UQ in Maxwell equations
Literature- K. Beddek, Y. Le Menach, S. Clenet, and O. Moreau. 3-d stochastic spectral finite- element method in static electromagnetism using vector potential formulation. Mag- netics, IEEE Transactions on, 47(5):1250–1253, May 2011
- J. Castrillón-Candás, F. Nobile, and R. Tempone. Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations. Computers and Mathematics with Applications, 71(6):1173–1197, 2016.
- C.Chauvière,J.S.Hesthaven,andL.Lurati.Computational modeling of uncertainty in time-domain electromagnetics. SIAM J. Sci. Comput., 28(2):751–775, 2006.
- Cohen, Albert; Devore, Ronald; Schwab, Christoph Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDE's
- Dick, Josef; Gantner, Robert N.; Le Gia, Quoc T.; Schwab, Christoph Multilevel higher-order quasi-Monte Carlo Bayesian estimation. Math. Models Methods Appl. Sci. 27 (2017), no. 5, 953–995. 
- Gantner, Robert N.; Schwab, Christoph Computational higher order quasi-Monte Carlo integration. Monte Carlo and quasi-Monte Carlo methods, 271–288, Springer Proc. Math. Stat., 163, 
-  Harbrecht, Helmut; Schneider, Reinhold; Schwab, Christoph Sparse second moment analysis for elliptic problems in stochastic domains. Numer. Math. 109 (2008), no. 3,
- Hiptmair, R., Scarabosio, L., Schillings, C. et al. Adv Comput Math (2018). 
- Jerez-Hanckes, Carlos; Schwab, Christoph; Zech, Jakob Electromagnetic wave scattering by random surfaces: shape holomorphy. Math. Models Methods Appl. Sci. 27 (2017), no. 12,2229–2259
- Jerez-Hanckes, Carlos; Schwab, Christoph Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements, IMA J. Numer. Anal. 37 (2017), no. 3, 1175–1210
- von Petersdorff, Tobias; Schwab, Christoph Sparse finite element methods for operator equations with stochastic data. Appl. Math. 51 (2006), no. 2, 145–180.
Prerequisites / Notice- Assistance is mandatory
- Students will choose 1 or 2 articles for presenting
- Individual meetings with lecturer will be scheduled on ad hoc basis
401-4671-00LAdvanced Numerical Methods for CSE9 credits4V + 2U + 1PR. Hiptmair, C. Jerez Hanckes
AbstractThis course discusses modern numerical methods involving complex algorithms and intricate data structures that render an efficient implementation non-trivial. The focus will be on boundary element methods, hierarchical matrix techniques, convolution quadrature, and algebraic multigrid methods.
Objective- Appreciation of the interplay of functional analysis, advanced calculus, numerical linear algebra, and sophisticated data structures in modern computer simulation technology.
- Knowledge about the main ideas and mathematical foundations underlying boundary element methods, hierarchical matrix techniques, convolution quadrature, and reduced basis methods.
- Familiarity with the algorithmic challenges arising with these methods and the main ways on how to tackle them.
- Knowledge about the algorithms' complexity and suitable data structures.
- Ability to understand details of given implementations.
- Skills concerning the implementation of algorithms and data structures in C++.
Content1 Boundary Element Methods (BEM)
1.1 Elliptic Model Boundary Value Problem: Electrostatics . . . . . . . .
1.2 Boundary Representation Formulas . . . . . . . . . . . . . . . . . .
1.3 Boundary Integral Equations (BIEs) . . . . . . . . . . . . . . . . . .
1.4 Boundary Element Methods in Two Dimensions . . . . . . . . . . . . . . . . . . .
1.5 Boundary Element Methods on Closed Surfaces . . . . . . . . . . . . . . . . . . .
1.6 BEM: Various Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Local Low-Rank Compression of Non-Local Operators
2.1 Examples: Non-Local Operators . . . . . . . . . . . . . . . . . . . . .
2.2 Approximation of Kernel Collocation Matrices . . . . . . . . . . . . . . .
2.3 Clustering Techniques . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Hierarchical Matrices . . . . . . . . . . . . . . . . . . .
3 Convolution Quadrature
3.1 Basic Concepts and Tools
3.2 Convolution Equations: Examples . . . . . . . . . . . . . .
3.3 Implicit-Euler Convolution Quadrature . . . . . . . . . . . .
3.5 Runge-Kutta Convolution Quadrature . . . . . . . . . . . .
3.6 Fast Oblivious Convolution Quadrature . . . . . . . .
4 Algebraic Multigrid Methods
Lecture notesLecture material will be created during the course and will be made available online and in chapters.
LiteratureS. Sauter and Ch. Schwab, Boundary Element Methods, Springer 2010
O. Steinbach, Numerical approximation methods for elliptic boundary value problems, Springer 2008
M. Bebendorf, Hierarchical matrices: A means to efficiently solve elliptic boundary value problems, Springer 2008
W. Hackbusch, Hierarchical Matrices, Springer 2015
S. Boerm, Efficient Numerical Methods for Non-Local Operators: H2-Matrix Compression, Algorithms and Analysis, EMS 2010
S. Boerm, Numerical Methods for Non-Local Operators, Lecture Notes Univ. Kiel 2017
M. Hassell and F.-J. Sayas, Convolution Quadrature for Wave Simulations
J.-C. Xu and L. Zikatanov, Algebraic Multirgrid Methods, Acta Numerica, 2017
Ch. Wagner, Introduction to Algebraic Multigrid, Lecture notes IWR Heidelberg, 1999, https://perso.uclouvain.be/alphonse.magnus/num2/amg.pdf
Prerequisites / Notice- Familiarity with basic numerical methods
(as taught in the course "Numerical Methods for CSE").
- Knowledge about the finite element method for elliptic partial differential equations (as covered in the course "Numerical Methods for Partial Differential Equations").
401-5650-00LZurich Colloquium in Applied and Computational Mathematics Information 0 credits2KR. Abgrall, R. Alaifari, H. Ammari, R. Hiptmair, A. Jentzen, C. Jerez Hanckes, S. Mishra, S. Sauter, C. Schwab
AbstractResearch colloquium
Objective