MAI0106 Lecture content
Lecture 1
Introduction. General principles and ideas.Notes here.
Lecture 2-3
Periodic solutions and Fourier analysis. The Petrovski condition for PDE and the von Neumann condition for difference schemes. (Sec. 2.1-2.2)Notes on the continuous problem here, notes on the discrete problem here.
Lecture 4-6
The energy method. Semi-bounded operators. Symmetric and skewsymmetric operators. (Sec. 2.3) Notes for lecture 4,5,6 follows here, here and here.Lecture 7-9
Normal mode analysis. The Kreiss condition. (Sec. 2.4 + Handouts)
Lecture 10
Well-posed boundary conditions in practise. Handouts-1, Handouts-2, Handouts-3
Lecture 11
The error equation. Energy estimates. Accuracy of discrete approximation. Unceartainty in data. Initial and boundary conditions. (Sec. 3.1-3.2 + Handouts)
Lecture 12
Effectiveness of high order schemes. (Sec. 1.1-1.2)
Lecture 13
Approximation in space. Standard and staggered grids. Pade type difference operators. (Sec. 4.1-4.3)
Lecture 14
Approximation in time. The test equation. Runge-Kutta and linear multi-step methods. The Lax-Wendroff principle.(Sec 5.1-5.3,6.1)
Lecture 15-16
Boundary treatment. Summation by parts (SBP) operators. Weak boundary conditions. Strict/time stability. (Sec. 7.1-7.4 + Handouts_1 + Handouts_2)
Lecture 17-18
Structured multi-block methods. Unstructured finite volume methods and discontinuous Galerkin methods. Stability and conservation. (Sec. 12.2 + Handouts_1 + Handouts_2 + Handouts_3 + Handouts_4)
Related Material
A lecture schedule for CME326 is given here.
Sidansvarig: jan.nordstrom@liu.se
Senast uppdaterad: 2019-11-29