Lecturer

Christoph Schwab (christoph.schwab at sam.math.ethz.ch )

Coordinator

Lukas Herrmann (lukas.herrmann at sam.math.ethz.ch)

First meeting to distribute topics: Thu Feb 22, 2018, 15:15 -- 17:00, HG D1.1

Descripton

The Seminar will address recently developed quasi-Monte Carlo methods for the numerical solution of high-dimensional integrals and their application to problems arise from PDEs with random input, based on several recent research papers.

Prerequisites

• Completed BSc exams in MATH or RW/CSE.

Performance Assessment

To earn seminar credits the student must:

• Prepare a 45 min presentation of the selected topic (Date and Time TBD).
• Prepare a written report ("Ausarbeitung") in Latex.

Literature:

• Leobacher, G.; Pillichshammer, F.: Introduction to quasi-Monte Carlo integration and applications. Compact Textbooks in Mathematics. Birkhäuser/Springer, Cham, 2014.
• Dick, J.; Kuo, F.Y.; Sloan, I.H.: High-dimensional integration: the quasi-Monte Carlo way. Acta Numer. 22 (2013), 133–288.
• Kuo, F.Y.; Schwab, Ch.; Sloan, I.H.: Quasi-Monte Carlo finite element methods for a class of elliptic partial differential equations with random coefficients. SIAM J. Numer. Anal. 50 (2012), no. 6, 3351–3374.
• Kuo, F.Y.; Schwab, Ch.; Sloan, I.H.: Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients. Found. Comput. Math. 15 (2015), no. 2, 411–449.
• Gantner, R.N.; Herrmann, L.; Schwab, Ch.: Quasi–Monte Carlo Integration for Affine-Parametric, Elliptic PDEs: Local Supports and Product Weights. SIAM J. Numer. Anal. 56 (2018), no. 1, 111–135.
• Gantner, R.N.; Herrmann, L.; Schwab, Ch.: Multilevel QMC with Product Weights for Affine-Parametric, Elliptic PDEs, in Comtemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan, J. Dick, F. Y. Kuo, and H. Woźniakowski, eds., Springer-Verlag, Cham, 2018, https://doi.org/10.1007/978-3-319-72456-0 18.
• Goda, T.; Dick, J.: Construction of interlaced scrambled polynomial lattice rules of arbitrary high order. Found. Comput. Math. 15 (2015), no. 5, 1245–1278.
• Dick, J.; Goda, T.; Suzuki, K.; Yoshiki, T.: Construction of interlaced polynomial lattice rules for infinitely differentiable functions. Numer. Math. 137 (2017), no. 2, 257–288.