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Lectu re Notes in Economics and Mathematical Systems

Fast Marching Methods are numerical schemes for computing solutions to the nonlinear Eikonal equation and related static Hamilton--Jacobi equations Based on entropy-satisfying upwind schemes and fast sorting techniques, they yield consistent, accurate, and highly efficient algorithms They are optimal in the sense that the computational complexity of the algorithms is O(N log N), where N is the total number of points in the domain The schemes are of use in a variety of applications, including problems in shape offsetting, computing distances from complex curves and surfaces, shape-from-shading, photolithographic development, computing first arrivals in seismic travel times, construction of shortest geodesics on surfaces, optimal path planning around obstacles, and visibility and reflection calculations In this paper, we review the development of these techniques, including the theoretical and numerical underpinnings; provide details of the computational schemes, including higher order versions; and demonstrate the techniques in a collection of different areas

Fast Marching Methods

Keywords: methodes : numeriques ; programmation ; differences : finies ; methode : integrale ; ecoulement : incompressible ; ecoulement : compressible ; ecoulement : visqueux ; mecanique des : fluides ; viscosite Reference Record created on 2005-11-18, modified on 2016-08-08

Computational methods for fluid flow

The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [1] and Garabedian [2].1 While it is admitted that the main idea to be used is more in the nature of a lucky guess than of a method, it will be found that the gain in brevity and simplicity of the argument is considerable. As a by-product, we shall also obtain a number of hitherto unknown identities between various domain functions. The basic problem treated in the above-mentioned papers is the following generalization of the classical Schwarz lemma: Given a finite schlicht domain D of connectivity n (n> 1) in the complex zplane and a point r in D, to find a function F(z) with the following properties: (a) F(z) belongs to the family B of analytic functions f(z) which are single-valued and regular in D and satisfy there If(z) I _ 1; (b) I F'(r) I > lf'(r) J, where f(z) is any function in B. Evidently, it is sufficient to solve this problem for any domain D' which is conformally equivalent to D. In particular, we may therefore assume, without restricting the generality of what follows, that D is bounded by analytic curves. It was shown by Ahlfors that F(z) yields a (1, n) conformal mapping of D onto the interior of the unit circle and that n-I of the n zeros of F(z) coincide with the zeros of a single-valued function h(z) which is regular in D with the exception of a simple pole at z = and satisfies -'ih(z)dz>O on the boundary r of D; the nth zero of F(z) is located at zx=. It was subsequently noticed by Garabedian that the function h(z) can be written in the form h(z) = F(z)q(z) where q(z) (Z )-2 is regular in D and that the extremal property of F(z) can be deduced in a very elegant manner from the resulting inequality

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On bounded analytic functions

The method of power series Equations of the first order Classification of partial differential equations Cauchy's problem for equations with two independent variables The fundamental solution Cauchy's problem in space of higher dimension The Dirichlet and Neumann problems Dirichlet's principle Existence theorems of potential theory Integral equations Eigenvalue problems Tricomi's problem formulation of well posed problems Finite differences Fluid dynamics Free boundary problems Partial differential equations in the complex domain Bibliography Index.

Partial Differential Equations

Supercritical Wing Sections II

An integrated study of compact stellarator power plants, ARIES-CS, has been conducted to explore attractive compact stellarator configurations and to define key research and development (R&D) areas The large size and mass predicted by earlier stellarator power plant studies had led to cost projections much higher than those of the advanced tokamak power plant As such, the first major goal of the ARIES-CS research was to investigate if stellarator power plants can be made to be comparable in size to advanced tokamak variants while maintaining desirable stellarator properties As stellarator fusion core components would have complex shapes and geometry, the second major goal of the ARIES-CS study was to understand and quantify, as much as possible, the impact of the complex shape and geometry of fusion core components This paper focuses on the directions we pursued to optimize the compact stellarator as a fusion power plant, summarizes the major findings from the study, highlights the key design aspects and constraints associated with a compact stellarator, and identifies the major issues to help guide future R&D

http://www-ferp.ucsd.edu/najmabadi/PAPER/A1-101-08-FST.pdf

The aries-cs compact stellarator fusion power plant

A numerical method to study plasma confinement in a strong magnetic field is detailed. The emphasis is on confinement in toroidal geometry without two-dimensional symmetry. The mathematical model employed in the investigation is based on the partial differential equations of ideal magnetohydrodynamics. The principal application is to stellarators, currently important in the development of controlled thermonuclear fusion. The BETA computer code, along with a sample run, is included.

Magnetohydrodynamic Equilibrium and Stability of Stellarators

A numerical method is developed for the solution of the magnetostatic equations. A computer code based on this method is used for the study of practical questions of equilibrium and stability in plasma physics. (MOW)

Paul Garabedian

Papers

Partial Differential Equations

Supercritical Wing Sections II

The aries-cs compact stellarator fusion power plant

Magnetohydrodynamic Equilibrium and Stability of Stellarators

A computational method in plasma physics