MAI0129 Course Information

Course Aims

The course intends to give the student knowledge about

• Why one needs uncertainty quantication when dealing with partial differential equations (PDEs).
• Intrusive methods: how one represents random fields via spectral expansions in PDEs.
• Linear initial boundary value problems with random data.
• Non-intrusive methods: how one computes statistics without spectral expansions.
• Nonlinear problems (the Burgers equation).
• Advanced topics: sensitivity of different PDEs, multiple stochastic dimensions, alternative basis.

Course Litterature

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, Nordstrom, 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 Quantifcation, 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. For parts of the course not covered by this material, relevant handouts and slides will be provided during the lectures.

Examination

Mandatory assignments to be done as home work. Approved assignments will give 5 Bologna points.

Page responsible: jan.nordstrom@liu.se
Last updated: 2019-11-29