Schnelle iterative Löser diskretisierter PDGln

Prof. Dr. Arnold Reusken ✉

Termine

Course description

The topic of this course is in the field of numerical treatment of partial differential equations (PDEs). In methods for the numerical solution of PDEs one typically distinguishes two main components. First one has to discretize the PDE using for example a finite difference, finite volume or finite element method. The discretization very often results in a very large linear system of equations that may have many millions of unknowns. The second component of the numerical solution process is the computation of the solution of this linear system. The second component almost always determines the computational time needed for the whole solution process. In practical applications, using a standard Gaussian elimination for solving the linear system leads to unacceptable computing times. Certain classes of iterative methods are much more efficient for these large discretization systems. In this course we will treat several classes of such iterative methods. These methods will be derived and key properties related to rate of convergence and efficiency are mathematically analyzed. We consider applications to for example the Poisson equation, the heat equation and the Stokes problem. It is assumed that the attendees are familiar with basic concepts of discretization methods (e.g., finite differences of finite elements) for PDEs.

Moodle - Lernraum

• Link zum Lernraum

Hinweise zur Übung

• Zur Bearbeitung der Programmieraufgaben wird Matlab benötigt