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Triangulations and Simplicial Methods

2012-12-06 Business & Economics
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Release : 2012-12-06
Genre : Business & Economics
Kind : eBook
Book Rating : 750/5 ( reviews)

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Book Synopsis Triangulations and Simplicial Methods by : Chuangyin Dang

Download or read book Triangulations and Simplicial Methods written by Chuangyin Dang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations underlying them. This monograph describes some recent developments in triangulations and simplicial methods. It includes the D1-triangulation and its applications to simplicial methods. As a result, efficiency of simplicial methods has been improved significantly. Thus more effective simplicial methods have been developed.

Recent Advances in Nonsmooth Optimization

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 659/5 ( reviews)

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Book Synopsis Recent Advances in Nonsmooth Optimization by : Dingzhu Du

Download or read book Recent Advances in Nonsmooth Optimization written by Dingzhu Du. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.

Simplicial Partitions with Applications to the Finite Element Method

2020-10-05 Mathematics
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Release : 2020-10-05
Genre : Mathematics
Kind : eBook
Book Rating : 778/5 ( reviews)

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Book Synopsis Simplicial Partitions with Applications to the Finite Element Method by : Jan Brandts

Download or read book Simplicial Partitions with Applications to the Finite Element Method written by Jan Brandts. This book was released on 2020-10-05. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on the mathematical and numerical analysis of simplicial partitions and the finite element method. This active area of research has become an essential part of physics and engineering, for example in the study of problems involving heat conduction, linear elasticity, semiconductors, Maxwell's equations, Einstein's equations and magnetic and gravitational fields. These problems require the simulation of various phenomena and physical fields over complicated structures in three (and higher) dimensions. Since not all structures can be decomposed into simpler objects like d-dimensional rectangular blocks, simplicial partitions are important. In this book an emphasis is placed on angle conditions guaranteeing the convergence of the finite element method for elliptic PDEs with given boundary conditions. It is aimed at a general mathematical audience who is assumed to be familiar with only a few basic results from linear algebra, geometry, and mathematical and numerical analysis.

The Geometry of Dynamical Triangulations

2009-02-17 Science
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Release : 2009-02-17
Genre : Science
Kind : eBook
Book Rating : 277/5 ( reviews)

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Book Synopsis The Geometry of Dynamical Triangulations by : Jan Ambjorn

Download or read book The Geometry of Dynamical Triangulations written by Jan Ambjorn. This book was released on 2009-02-17. Available in PDF, EPUB and Kindle. Book excerpt: The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

2008-06-25 Mathematics
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Release : 2008-06-25
Genre : Mathematics
Kind : eBook
Book Rating : 09X/5 ( reviews)

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Book Synopsis Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by : Tarek Mathew

Download or read book Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations written by Tarek Mathew. This book was released on 2008-06-25. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.

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