Read e-book online Adaptive Moving Mesh Methods PDF

By Weizhang Huang

ISBN-10: 1441979158

ISBN-13: 9781441979155

ISBN-10: 1441979166

ISBN-13: 9781441979162

Moving mesh equipment are an efficient, mesh-adaptation-based strategy for the numerical answer of mathematical types of actual phenomena. at the moment there exist 3 major thoughts for mesh variation, particularly, to take advantage of mesh subdivision, neighborhood excessive order approximation (sometimes mixed with mesh subdivision), and mesh move. The latter kind of adaptive mesh process has been much less good studied, either computationally and theoretically.

This publication is set adaptive mesh new release and relocating mesh tools for the numerical resolution of time-dependent partial differential equations. It provides a normal framework and idea for adaptive mesh iteration and offers a complete therapy of relocating mesh equipment and their easy elements, besides their program for a few nontrivial actual difficulties. Many specific examples with computed figures illustrate a number of the tools and the consequences of parameter offerings for these equipment. The partial differential equations thought of are typically parabolic (diffusion-dominated, instead of convection-dominated).

The large bibliography offers a useful advisor to the literature during this box. each one bankruptcy includes invaluable routines. Graduate scholars, researchers and practitioners operating during this region will reap the benefits of this book.

Weizhang Huang is a Professor within the division of arithmetic on the collage of Kansas.

Robert D. Russell is a Professor within the division of arithmetic at Simon Fraser University.

Show description

Read or Download Adaptive Moving Mesh Methods PDF

Similar counting & numeration books

New PDF release: Upscaling multiphase flow in porous media: from pore to core

This e-book presents concise, up to date and easy-to-follow info on sure elements of an ever vital examine sector: multiphase stream in porous media. This stream kind is of significant importance in lots of petroleum and environmental engineering difficulties, reminiscent of in secondary and tertiary oil restoration, subsurface remediation and CO2 sequestration.

Computational Methods for Physicists: Compendium for by Simon Sirca, Martin Horvat PDF

This ebook is helping complicated undergraduate, graduate and postdoctoral scholars of their day-by-day paintings via delivering them a compendium of numerical equipment. the alternative of equipment can pay major realization to errors estimates, balance and convergence concerns in addition to to the how one can optimize software execution speeds.

Read e-book online Derivative Securities and Difference Methods PDF

This e-book is dedicated to deciding upon the costs of monetary derivatives utilizing a partial differential equation process. within the first half the authors describe the formula of the issues (including comparable free-boundary difficulties) and derive the closed shape ideas in the event that they were came across. the second one half discusses the way to receive their numerical options successfully for either European-style and American-style derivatives and for either inventory techniques and rate of interest derivatives.

New PDF release: Numbers and Computers

It is a publication approximately numbers and the way these numbers are represented in and operated on by means of pcs. it's important that builders comprehend this sector as the numerical operations allowed through pcs, and the constraints of these operations, specifically within the sector of floating element math, impact nearly every little thing humans try and do with pcs.

Extra info for Adaptive Moving Mesh Methods

Sample text

Iteration is normally required to obtain a good approximation to the equidistributing mesh associated with the underlying mesh density function ρ = ρ(x). A simple iteration procedure is to let the current approximation now be the background mesh and to use the nodal values of the mesh density function on it to generate a new mesh. A sequence (n) of meshes of N points, {Tˆh }∞ n=0 , can be generated this way. , N ρ(xˆ j−1 ) + ρ(xˆ j ) . 23) provided that the mesh density function is sufficiently smooth and N is sufficiently large.

A natural and important approach for designing this type of algorithm is the variational approach for which the mesh point relocation and movement are determined by minimizing some functional formulated to measure error or difficulty in numerical simulation. Many location-based algorithms have been developed as variational ones, whereas some others have been based on elliptic PDEs or other considerations. For example, Winslow [341] and Thompson et al. [324] use a system of elliptic PDEs for generating boundary-fitted meshes.

44)         .    ∗  ..  ∗ 16 1 Introduction (a) Computed solution. (b) Mesh trajectories. 9 1 Fig. 0. (b) The corresponding mesh trajectories. 9 1 Fig. 8 The time step size used in the adaptive moving mesh solution of Burgers’ equation with ε = 10−4 and 61 points is plotted as function of time. The relative and absolute tolerances for the time step control are taken as rtol = 10−6 and atol = 10−4 , respectively, for the Matlab ODE solver “ode15i” (using a backward differentiation formula of order 5).

Download PDF sample

Adaptive Moving Mesh Methods by Weizhang Huang


by Paul
4.3

Rated 4.49 of 5 – based on 25 votes