arXiv subjects
Publications and source records attributed to Martin Bäker.
This document is a short and informal tutorial on some aspects of calculating phase diagrams with the ATAT-tools emc2 and phb and on creating cluster expansions with maps. It is neither complete, nor in any way an official document, but mainly a set of collected notes I took during experimentation with ATAT.
This document gives guidelines to set up, run, and postprocess correct simulations with the finite element method. It is not an introduction to the method itself, but rather a list of things to check and possible mistakes to watch out for when doing a finite element simulation.
The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large, the modes thus identified can be used to strongly improve the convergence. The method presented here is applicable to any standard algorithm like Conjugate Gradient, relaxation or multigrid. An example from theoretical physics, the Dirac equation in the presence of almost-zero modes arising from instantons, is studied. Using the principle, bad-converging modes are removed efficiently. Applied locally, the principle is one of the main ingredients of the Iteratively Smooting Unigrid algorithm.
We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal with these modes, shows no critical slowing down for this problem.