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1	A parallel adaptive method for pseudo-arclength continuation Dubitski, Alexander 01 August 2011 (has links) We parallelize the pseudo-arclength continuation method for solving nonlinear systems of equations. Pseudo-arclength continuation is a predictor-corrector method where the correction step consists of solving a linear system of algebraic equations. Our algorithm parallelizes adaptive step-length selection and inexact prediction. Prior attempts to parallelize pseudo-arclength continuation are typically based on parallelization of the linear solver which leads to completely solver-dependent software. In contrast, our method is completely independent of the internal solver and therefore applicable to a large domain of problems. Our software is easy to use and does not require the user to have extensive prior experience with High Performance Computing; all the user needs to provide is the implementation of the corrector step. When corrector steps are costly or continuation curves are complicated, we observe up to sixty percent speed up with moderate numbers of processors. We present results for a synthetic problem and a problem in turbulence. / UOIT HPC Arclength Parallel Computing
2	Grundläggande hyperbolisk geometri / Elements of Hyperbolic Geometry Persson, Anna January 2006 (has links) <p>I denna uppsats presenteras grundläggande delar av hyperbolisk geometri. Uppsatsen är indelad i två kapitel. I första kapitlet studeras Möbiusavbildningar på Riemannsfären. Andra kapitlet presenterar modellen av hyperbolisk geometri i övre halvplanet H, skapad av Poincaré på 1880-talet.</p><p>Huvudresultatet i uppsatsen är Gauss – Bonnét´s sats för hyperboliska trianglar.</p> / <p>In this thesis we present fundamental concepts in hyperbolic geometry. The thesis is divided into two chapters. In the first chapter we study Möbiustransformations on the Riemann sphere. The second part of the thesis deal with hyperbolic geometry in the upper half-plane. This model of hyperbolic geometry was created by Poincaré in 1880.</p><p>The main result of the thesis is Gauss – Bonnét´s theorem for hyperbolic triangles.</p> Hyperbolic Geometry Möbius transformation Gauss-Bonnét Geodetic line isometry rotation translation cross-ratio hyperbolic arclength Hyperbolisk geometri Möbiusavbildningar Gauss-Bonnét geodetisk linje isometri rotation translation anharmoniskt förhållande hyperbolisk båglängd MATHEMATICS MATEMATIK
3	Grundläggande hyperbolisk geometri / Elements of Hyperbolic Geometry Persson, Anna January 2006 (has links) I denna uppsats presenteras grundläggande delar av hyperbolisk geometri. Uppsatsen är indelad i två kapitel. I första kapitlet studeras Möbiusavbildningar på Riemannsfären. Andra kapitlet presenterar modellen av hyperbolisk geometri i övre halvplanet H, skapad av Poincaré på 1880-talet. Huvudresultatet i uppsatsen är Gauss – Bonnét´s sats för hyperboliska trianglar. / In this thesis we present fundamental concepts in hyperbolic geometry. The thesis is divided into two chapters. In the first chapter we study Möbiustransformations on the Riemann sphere. The second part of the thesis deal with hyperbolic geometry in the upper half-plane. This model of hyperbolic geometry was created by Poincaré in 1880. The main result of the thesis is Gauss – Bonnét´s theorem for hyperbolic triangles. Hyperbolic Geometry Möbius transformation Gauss-Bonnét Geodetic line isometry rotation translation cross-ratio hyperbolic arclength Hyperbolisk geometri Möbiusavbildningar Gauss-Bonnét geodetisk linje isometri rotation translation anharmoniskt förhållande hyperbolisk båglängd MATHEMATICS MATEMATIK

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