ISU - Multigrid for computing propagators

The Iteratively Smoothing Unigrid algorithm (ISU), a new multigrid method for computing propagators in Lattice Gauge Theory, is explained. The main idea is to compute good (i.e.\ smooth) interpolation operators in an iterative way. This method shows {\em no critical slowing down} for the 2-dimensional Laplace equation in an SU(2) gauge field. First results for the Dirac-operator are also shown.Comment: 3 pages, latex, no figures, Contribution to Lattice 94, uses espcrc2.sty and fleqn.sty as required for lattice proceeding

The principle of indirect elimination

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.Comment: 16 pages, LaTeX-style espart (elsevier preprint style). Three .eps-figures are now added with the figure command

Localization in Lattice Gauge Theory and a New Multigrid Method

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.Comment: LATeX style, 11 pages (plus 4 figure pages). Figure pages are available as uuencoded ps-file via anonymous ftp from x4u2.desy.de, get pub/outgoing/baeker/heplat.uu. DESY-preprint 94-07

On the Cox ring of blowing up the diagonal

We compute the Cox rings of the blow-ups $\mathrm{Bl}_\Delta(X'\times X')$ and $\mathrm{Bl}_\Delta(\mathbb P_1^n)$ where $X'$ is a product of projective spaces and $\Delta$ is the (generalised) diagonal.Comment: 8 page

An Investigation of the Chip Segmentation Process Using Finite Elements

A finite element model of a two-dimensional orthogonal metal cutting process is used to simulate the formation of segmented chips. The deformation of the chip during segmentation is studied and the distribution of deformation energy in chip and shear band is analyzed. It is shown that the plastic deformation both in the shear band and the segment contribute significantly to the cutting force. A variation of the thermal conductivity strongly affects the segmentation and indicates that segmentation is energetically favorable