Learn the concepts of Multigrid/Multilevel methods, and their application and implementation for optimally efficient numerical simulation of problems and phenomena in physics and engineering sciences.|
Simulations by computer nowadays play an important role in the technical and physical sciences, both in research as well as in design. Examples are the fields of structural and fluid mechanics where the behaviour of structures and flows are simulated based on the Navier-Cauchy equations and the Navier-Stokes equations. The introduction and further development of the digital computer has given rise to an entire field nowadays referred to as scientific computing (Computational Mechanics, Computational Fluid Dynamics). Other examples are the simulations baed on particles, in physics, and protein folding in biological and pharmaceutical applications, and image analysis in vision and medical diagnostics. In most applications the computer models exploit the known behaviour on a small scale (particle motion, or discrete equation) to simulate problems on a large scale. The advantage of the computer is then, hopefully, that large systems can be considered. However, in many cases, owing to some characteristic slowness resulting from the scale difference between the local equation and the size of the system (and accuracy required) standard algorithms for “solving” the system are extremely slow to converge, and lead to excessive computing times which seriously hampers the potential of real application of these models in an engineering environment for actual design. Multgrid/Multilevel methods are a concept by which the different scales of behaviour in a problem are efficiently exploited to design optimally efficient numerical algorithms. Since their introduction for solving Partial Differential Equations in the 1980-1990’s these methods have had an enormous impact on many fields in science and engineering. They have led to very fast solvers, enabling the analysis of much more complex and realistic problems, as well as the capability to perform advanced analysis on small scale computers in acceptable times.|
In recent years the computer capacity has increased enormously. However, the need for fast and efficient solvers is bigger than ever. In this course the student learns the concept of Multigrid/Multilevel methods and the actual application of this concept for typical problems encountered in the physical and engineering sciences, by actually “doing it yourself”.