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V5E3: Advanced Topics in Scientific Computing
The numerical simulation of physical systems leads to several challenges when the simulation is supposed to be realistic: (a) The shape of the domain is usually three-dimensional and not just a simple cube, (b) the discretization with high resolution lead to systems of equations with a lot of unknowns (say 1e10), and (c) the resolution may need to be finer in some areas of the domain than in others (d) and the areas of highest resolution may move with time. Examples are the stress analysis of a bridge or skyscraper and the tracking of flames or shocks in gases, as well as geophysical simulations (of mantle convection or earthquakes).
In this lecture we will assume that the finite element or finite volume method to solve a basic partial differential equation (such as Poisson's) is understood on a cubic domain. We will revisit the basics and then move on to the topics of mesh generation (addressing a), parallelization and scalable solvers (b) and adaptivity (c, d).
This lecture will expand the students' knowledge on computational geometry, high performance computing and state-of-the art techniques for adaptive mesh refinement. We may occasionally discuss selected research papers as part of the lecture. A useful book on mesh generation is "Grid Generation Methods" by V.D. Liseikin.
The lectures Wissenschaftliches Rechnen I (V3E1/F4E1) as well as one class out of Wissenschaftliches Rechnen II (V3E2/F4E2), Numerical Simulation (V4E1) or Numerical Algorithms (V4E2) are prerequisites. We may discuss the requirements further in the first lecture.
The lecture takes place on Mondays and Thursdays at 14 Uhr c.t. in We6 6.020.
There are no exercises outside of the lecture slots. We may sometimes convert a lecture slot to exercises in the computer room. There will be an oral exam between July 31st and August 3rd and on September 27th and 28th.
Please read the coding guidelines. For those who have begun working on a programming exercise, please email me a header file and at least a source file with a dummy function that does nothing but compiles cleanly.