Polopoly kommer stängas 15 december 2023. Innan dess behöver kvarvarande sidor flyttas eller tas bort. Medarbetare kan läsa mer på FAQ Polopoly Avveckling
Den efterfrågade sidan finns ej på det önskade språket.
Den efterfrågade artikeln finns för dessa språk..
MAI0129
Stochastic Galerkin Methods for Partial Differential Equations
Number of credits: 5 hp
Examiner: Jan Nordström
Course literature:
GX08: Gottlieb, Xiu, Galerkin Method for Wave Equations with Uncertain Coefficients, Commun. Comput. Phys., Vol. 3, No. 2, pp. 505-518, 2008.
PIN15: Pettersson, Iaccarino, Nordström, Polynomial Chaos Methods for Hyperbolic Partial Differential Equations, Springer, 2015.
TPME11: Tuminaro, Phipps, Miller, Elman, Assessment of Collocation and Galerkin Approaches to Linear Diffusion Equations with Random Data, International Journal for Uncertainty Quantification, Vol. 1, No. 1, pp. 19-33, 2011.
XK02: Xiu, Karniadakis, Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos, CMAME, Vol. 191, pp. 49274948, 2002.
Course contents:
Basic Concepts
Introduction
Representation of random fields via spectral expansions:
PDE Theory
Reading Material: TPME11.
Linear Problems
Hyperbolic Problems
Parabolic Problems
Elliptic Problems
Reading Material: XK02, GX08
Non-intrusive Methods
Summary of the material from day 1-2
Non-intrusive methods
Reading material: TPME11
Nonlinear Problems (Burgers' equation)
Nonlinear analysis for stochastic problem guided by deterministic analysis
Analysis of the exact solution of the stochastic Burgers' equation
Introduction to project work/assignments
Reading material: PIN15 Ch. 6
Advanced topics
Sensitivity of different PDEs
Multiple stochastic dimensions
Alternative gPC basis functions: wavelets, spatially adaptive gPC
Organisation: Lectures and exercises, mixed.
Examination: Work in small groups (or individually) on a mini project. Project topics will be provided by the lecturers. The deliverables include a report (5 pages) and mandatory homework.
Prerequisites: Basic knowledge in computational mathematics and mathematical statistics.
Sidansvarig:
karin.johansson@liu.se
Senast uppdaterad: 2022-11-14