Göm meny

MAI0122 Lecture content

Lecture 1

Introduction. General principles and ideas. Well posed problems. Initial value problems. Periodic solutions and Fourier analysis. The Petrovski condition for PDE and the von Neumann condition for difference schemes.

Notes here.

Lecture 2

The initial boundary value problem. Well posed problems. The energy method. Semi-bounded operators. Semi-discrete approximations. Boundary conditions. Symmetric and skewsymmetric operators.

Notes here.

Lecture 3

High order finite difference approximations. Summation by parts (SBP) operators. Weak boundary conditions using the simultaneous approximation term (SAT) technique. Boundary conditions. SBP-SAT for examples.

Notes here.

Lecture 4

More on SBP-SAT techniques. Accuracy and errors estimates. Principles for construction of penalty terms. Penalty terms for hyperbolic and parabolic problems. SBP-SAT for multiblock methods. A roadmap for well posed and stable problems.

Notes here and here.

Lecture 5

Extension of SBP-SAT to multiple dimensions. Stability and conservation. Multi-block methods for SBP-SAT. Finite volume methods. Discontinuous Galerkin methods. Hybrid methods.

Notes here.

Lecture 6

Approximation in time. Focus on approximations in time from PDEs. Basic theory. Explicit Runge-Kutta methods. Dual time-stepping. Implicit contra explicit methods. Summation-by-parts in time

Notes here.

Related Material

A lecture schedule for CME326 is given here.

Sidansvarig: jan.nordstrom@liu.se
Senast uppdaterad: 2019-11-29