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Author : Andrey Martynenko
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.:/5 (65 download)
Download or read book Numerical Methods for Advection-diffusion Equations on Locally Refined Meshes written by Andrey Martynenko and published by . This book was released on 2004 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Torsten Linß
Publisher : Springer
ISBN 13 : 3642051340
Total Pages : 331 pages
Book Rating : 4.6/5 (42 download)
Download or read book Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems written by Torsten Linß and published by Springer. This book was released on 2009-11-21 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.
Author : Willem Hundsdorfer
Publisher : Springer Science & Business Media
ISBN 13 : 3662090171
Total Pages : 479 pages
Book Rating : 4.6/5 (62 download)
Download or read book Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations written by Willem Hundsdorfer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique book on Reaction-Advection-Diffusion problems
Author : Cornelis Boudewijn Vreugdenhil
Publisher :
ISBN 13 :
Total Pages : 396 pages
Book Rating : 4.F/5 ( download)
Download or read book Numerical Methods for Advection--diffusion Problems written by Cornelis Boudewijn Vreugdenhil and published by . This book was released on 1993 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Viktor A. Rukavishnikov
Publisher : MDPI
ISBN 13 : 3036503765
Total Pages : 128 pages
Book Rating : 4.0/5 (365 download)
Download or read book Mesh Methods written by Viktor A. Rukavishnikov and published by MDPI. This book was released on 2021-03-29 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.
Author : Hans Petter Langtangen
Publisher : Springer
ISBN 13 : 3319554565
Total Pages : 522 pages
Book Rating : 4.3/5 (195 download)
Download or read book Finite Difference Computing with PDEs written by Hans Petter Langtangen and published by Springer. This book was released on 2017-06-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
Author : Ivo Babuska
Publisher : Springer Science & Business Media
ISBN 13 : 1461242487
Total Pages : 487 pages
Book Rating : 4.4/5 (612 download)
Download or read book Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations written by Ivo Babuska and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.
Author : Tomasz Plewa
Publisher : Springer Science & Business Media
ISBN 13 : 3540270396
Total Pages : 550 pages
Book Rating : 4.5/5 (42 download)
Download or read book Adaptive Mesh Refinement - Theory and Applications written by Tomasz Plewa and published by Springer Science & Business Media. This book was released on 2005-12-20 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.
Author : Arlene Louise Perkins
Publisher :
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.:/5 (39 download)
Download or read book Parallel Heterogeneous Mesh Refinement for Multidimensional Convection-diffusion Equations Using an Euler-Lagrange Method written by Arlene Louise Perkins and published by . This book was released on 1989 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (727 download)
Download or read book Parallel Computation of Three-Dimensional Flows Using Overlapping Grids with Adaptive Mesh Refinement written by and published by . This book was released on 2007 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.
Author : Harendra Singh
Publisher : CRC Press
ISBN 13 : 1000381080
Total Pages : 337 pages
Book Rating : 4.0/5 (3 download)
Download or read book Advanced Numerical Methods for Differential Equations written by Harendra Singh and published by CRC Press. This book was released on 2021-07-29 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.
Author : Guy P. Brasseur
Publisher : Cambridge University Press
ISBN 13 : 1108210953
Total Pages : 631 pages
Book Rating : 4.1/5 (82 download)
Download or read book Modeling of Atmospheric Chemistry written by Guy P. Brasseur and published by Cambridge University Press. This book was released on 2017-06-19 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling of atmospheric composition is a formidable scientific and computational challenge. This comprehensive presentation of the modeling methods used in atmospheric chemistry focuses on both theory and practice, from the fundamental principles behind models, through to their applications in interpreting observations. An encyclopaedic coverage of methods used in atmospheric modeling, including their advantages and disadvantages, makes this a one-stop resource with a large scope. Particular emphasis is given to the mathematical formulation of chemical, radiative, and aerosol processes; advection and turbulent transport; emission and deposition processes; as well as major chapters on model evaluation and inverse modeling. The modeling of atmospheric chemistry is an intrinsically interdisciplinary endeavour, bringing together meteorology, radiative transfer, physical chemistry and biogeochemistry, making the book of value to a broad readership. Introductory chapters and a review of the relevant mathematics make this book instantly accessible to graduate students and researchers in the atmospheric sciences.
Author : Torsten Lin y
Publisher :
ISBN 13 : 9783642051531
Total Pages : 340 pages
Book Rating : 4.0/5 (515 download)
Download or read book Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems written by Torsten Lin y and published by . This book was released on 2009-11-22 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on numerical methods for singular perturbation problems - in particular, stationary reaction-convection-diffusion problems exhibiting layer behaviour is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. A classification and a survey of layer-adapted meshes for reaction-convection-diffusion problems are included. This structured and comprehensive account of current ideas in the numerical analysis for various methods on layer-adapted meshes is addressed to researchers in finite element theory and perturbation problems. Finite differences, finite elements and finite volumes are all covered.
Author : Douglas L. Dwoyer
Publisher :
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.:/5 (318 download)
Download or read book 11th International Conference on Numerical Methods in Fluid Dynamics written by Douglas L. Dwoyer and published by . This book was released on 1989 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with almost a hundred research communications this volume contains six invited lectures of lasting value. They cover modeling in plasma dynamics, the use of parallel computing for simulations and the applications of multigrid methods to Navier-Stokes equations, as well as other surveys on important techniques. An inaugural talk on computational fluid dynamics and a survey that relates dynamical systems, turbulence and numerical solutions of the Navier-Stokes equations give an exciting view on scientific computing and its importance for engineering, physics and mathematics.
Author : Philippe G. Ciarlet
Publisher : Gulf Professional Publishing
ISBN 13 : 9780444512246
Total Pages : 1187 pages
Book Rating : 4.5/5 (122 download)
Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 1187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications
Author : Sergey Repin
Publisher : Springer Science & Business Media
ISBN 13 : 9400752873
Total Pages : 446 pages
Book Rating : 4.4/5 (7 download)
Download or read book Numerical Methods for Differential Equations, Optimization, and Technological Problems written by Sergey Repin and published by Springer Science & Business Media. This book was released on 2012-10-13 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the results in numerical analysis and optimization presented at the ECCOMAS thematic conference “Computational Analysis and Optimization” (CAO 2011) held in Jyväskylä, Finland, June 9–11, 2011. Both the conference and this volume are dedicated to Professor Pekka Neittaanmäki on the occasion of his sixtieth birthday. It consists of five parts that are closely related to his scientific activities and interests: Numerical Methods for Nonlinear Problems; Reliable Methods for Computer Simulation; Analysis of Noised and Uncertain Data; Optimization Methods; Mathematical Models Generated by Modern Technological Problems. The book also includes a short biography of Professor Neittaanmäki.
Author : George Em Karniadakis
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571684
Total Pages : 360 pages
Book Rating : 4.1/5 (15 download)
Download or read book Numerical Methods written by George Em Karniadakis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-04-15 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.
