Space-Time Adaptive Numerical Methods

ISBN-13: 9783838106663 / Angielski / Miękka / 2009 / 200 str.

Sascha Schnepp

Opis

This work establishes techniques for adjusting the local spatial resolution ofselected numerical methods in a time-adaptive manner. Such techniques aredeveloped within the framework of the Finite Integration Technique (FIT), ahybrid Finite Integration-Finite Volume (FI-FV) Scheme and theDiscontinuous Galerkin Method (DGM). While the FIT and the DGM areestablished methods for the numerical solution of electromagnetic fieldproblems, the FI-FV Scheme is a novel method. The semi-discrete as well asthe fully discretized formulations of all considered methods are presented.For both formulations an analysis of the dispersive and dissipative behavioron fixed computational grids is carried out. As a result, asymptotic orders ofthe dispersion and dissipation errors are established. Techniques for thedetermination and modification of the discrete electromagnetic fieldquantities in locally refined regions are presented. The numerical stability ofthe developed adaptive methods is proven. The developed algorithms areapplied to the self-consistent simulation of charged particle dynamics andelectrodynamics.