Arbitrary black-string deformations in the black string-black hole transitions

We study the possible black string-black hole transition by analyzing the structure of the apparent horizon for a large family of time-symmetric initial data. We observe that, as judged by the apparent horizon, it is possible to generate arbitrarily deformed black strings at a moment of time symmetry. A similar study for hyperspherical black holes reveals that although arbitrarily deformed hyperspherical black holes can be constructed, the proper distance between the north and south poles along the extra direction has an upper limit.Comment: 10 pages, 7 figure

WPŁYW WARUNKU BRZEGOWEGO DIRICHLETA NA SZYBKOŚĆ I STABILNOŚĆ SYMULACJI PRĄDÓW WIROWYCH ELEKTRYCZNYM POTENCJAŁEM SKALARNYM

Field of presented results are bioelectromagnetic problems. Mathematical description of eddy-currents excited by external, low time-varying magnetic fields coming from the current flowing in the coil, was formulated on the basis of the electric scalar potential. This article shows effect of applies Dirichlet boundary condition to calculation rate and stability. Lots of numerical tests show that it is not always advisable.Polem zastosowań prezentowanych wyników są problemy bioelektromagnetyzmu. Matematyczny opis prądów wirowych, przy wolnozmiennych wymuszeniach elektromagnetycznych pochodzących od płynącego w cewce prądu elektrycznego, został sformułowany w oparciu o skalarny potencjał elektryczny. W artykule przedstawiono oddziaływanie zadawania zerowego warunku brzegowego Dirichleta na jakość i szybkość otrzymywania wyników. Szereg testów numerycznych wykazał, iż nie zawsze jest on wskazany

Automated code generation for discontinuous Galerkin methods

A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates efficient code in a standard programming language. This facilitates the rapid generation of efficient code for general equations in varying spatial dimensions. Key concepts underlying the compiler approach and the automated generation of computer code are elaborated. The approach is demonstrated for a range of common problems, including the Poisson, biharmonic, advection--diffusion and Stokes equations

Efficient Compilation of a Class of Variational Forms

We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler (FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC.Comment: ACM Transactions on Mathematical Software 33(3), 20 pages (2007