A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] /
The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. Up to now, however, meshfree methods have been in an early experimental stage and were not competitive due to the lack of efficient iterative solvers and numerical quadrature. This volume now presents an efficient parallel implementation of a meshfree method, namely the partition of unity method (PUM). A general numerical integration scheme is presented for the efficient assembly of the stiffness matrix as well as an optimal multilevel solver for the arising linear system. Furthermore, detailed information on the parallel implementation of the method on distributed memory computers is provided and numerical results are presented in two and three space dimensions with linear, higher order and augmented approximation spaces with up to 42 million degrees of freedom.
Main Authors: | , |
---|---|
Format: | Texto biblioteca |
Language: | eng |
Published: |
Berlin, Heidelberg : Springer Berlin Heidelberg,
2003
|
Subjects: | Mathematics., Mathematical analysis., Analysis (Mathematics)., Partial differential equations., Computer mathematics., Physics., Applied mathematics., Engineering mathematics., Analysis., Computational Mathematics and Numerical Analysis., Numerical and Computational Physics., Partial Differential Equations., Appl.Mathematics/Computational Methods of Engineering., |
Online Access: | http://dx.doi.org/10.1007/978-3-642-59325-3 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
KOHA-OAI-TEST:201483 |
---|---|
record_format |
koha |
spelling |
KOHA-OAI-TEST:2014832018-07-30T23:28:57ZA Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / Schweitzer, Marc Alexander. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg,2003.engThe numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. Up to now, however, meshfree methods have been in an early experimental stage and were not competitive due to the lack of efficient iterative solvers and numerical quadrature. This volume now presents an efficient parallel implementation of a meshfree method, namely the partition of unity method (PUM). A general numerical integration scheme is presented for the efficient assembly of the stiffness matrix as well as an optimal multilevel solver for the arising linear system. Furthermore, detailed information on the parallel implementation of the method on distributed memory computers is provided and numerical results are presented in two and three space dimensions with linear, higher order and augmented approximation spaces with up to 42 million degrees of freedom.1 Introduction -- 2 Partition of Unity Method -- 2.1 Construction of a Partition of Unity Space -- 2.2 Properties -- 2.3 Basic Convergence Theory -- 3 Treatment of Elliptic Equations -- 3.1 Galerkin Discretization -- 3.2 Boundary Conditions -- 3.3 Numerical Results -- 4 Multilevel Solution of the Resulting Linear System -- 4.1 Multilevel Iterative Solvers -- 4.2 Multilevel Partition of Unity Method -- 4.3 Numerical Results -- 5 Tree Partition of Unity Method -- 5.1 Single Level Cover Construction -- 5.2 Construction of a Sequence of PUM Spaces -- 5.3 Numerical Results -- 6 Parallelization and Implementational Details -- 6.1 Parallel Data Structures -- 6.2 Parallel Tree Partition of Unity Method -- 6.3 Numerical Results -- 7 Concluding Remarks -- Treatment of other Types of Equations -- A.1 Parabolic Equations -- A.2 Hyperbolic Equations -- Transformation of Keys -- Color Plates -- References.The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. Up to now, however, meshfree methods have been in an early experimental stage and were not competitive due to the lack of efficient iterative solvers and numerical quadrature. This volume now presents an efficient parallel implementation of a meshfree method, namely the partition of unity method (PUM). A general numerical integration scheme is presented for the efficient assembly of the stiffness matrix as well as an optimal multilevel solver for the arising linear system. Furthermore, detailed information on the parallel implementation of the method on distributed memory computers is provided and numerical results are presented in two and three space dimensions with linear, higher order and augmented approximation spaces with up to 42 million degrees of freedom.Mathematics.Mathematical analysis.Analysis (Mathematics).Partial differential equations.Computer mathematics.Physics.Applied mathematics.Engineering mathematics.Mathematics.Analysis.Computational Mathematics and Numerical Analysis.Numerical and Computational Physics.Partial Differential Equations.Appl.Mathematics/Computational Methods of Engineering.Springer eBookshttp://dx.doi.org/10.1007/978-3-642-59325-3URN:ISBN:9783642593253 |
institution |
COLPOS |
collection |
Koha |
country |
México |
countrycode |
MX |
component |
Bibliográfico |
access |
En linea En linea |
databasecode |
cat-colpos |
tag |
biblioteca |
region |
America del Norte |
libraryname |
Departamento de documentación y biblioteca de COLPOS |
language |
eng |
topic |
Mathematics. Mathematical analysis. Analysis (Mathematics). Partial differential equations. Computer mathematics. Physics. Applied mathematics. Engineering mathematics. Mathematics. Analysis. Computational Mathematics and Numerical Analysis. Numerical and Computational Physics. Partial Differential Equations. Appl.Mathematics/Computational Methods of Engineering. Mathematics. Mathematical analysis. Analysis (Mathematics). Partial differential equations. Computer mathematics. Physics. Applied mathematics. Engineering mathematics. Mathematics. Analysis. Computational Mathematics and Numerical Analysis. Numerical and Computational Physics. Partial Differential Equations. Appl.Mathematics/Computational Methods of Engineering. |
spellingShingle |
Mathematics. Mathematical analysis. Analysis (Mathematics). Partial differential equations. Computer mathematics. Physics. Applied mathematics. Engineering mathematics. Mathematics. Analysis. Computational Mathematics and Numerical Analysis. Numerical and Computational Physics. Partial Differential Equations. Appl.Mathematics/Computational Methods of Engineering. Mathematics. Mathematical analysis. Analysis (Mathematics). Partial differential equations. Computer mathematics. Physics. Applied mathematics. Engineering mathematics. Mathematics. Analysis. Computational Mathematics and Numerical Analysis. Numerical and Computational Physics. Partial Differential Equations. Appl.Mathematics/Computational Methods of Engineering. Schweitzer, Marc Alexander. author. SpringerLink (Online service) A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / |
description |
The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. Up to now, however, meshfree methods have been in an early experimental stage and were not competitive due to the lack of efficient iterative solvers and numerical quadrature. This volume now presents an efficient parallel implementation of a meshfree method, namely the partition of unity method (PUM). A general numerical integration scheme is presented for the efficient assembly of the stiffness matrix as well as an optimal multilevel solver for the arising linear system. Furthermore, detailed information on the parallel implementation of the method on distributed memory computers is provided and numerical results are presented in two and three space dimensions with linear, higher order and augmented approximation spaces with up to 42 million degrees of freedom. |
format |
Texto |
topic_facet |
Mathematics. Mathematical analysis. Analysis (Mathematics). Partial differential equations. Computer mathematics. Physics. Applied mathematics. Engineering mathematics. Mathematics. Analysis. Computational Mathematics and Numerical Analysis. Numerical and Computational Physics. Partial Differential Equations. Appl.Mathematics/Computational Methods of Engineering. |
author |
Schweitzer, Marc Alexander. author. SpringerLink (Online service) |
author_facet |
Schweitzer, Marc Alexander. author. SpringerLink (Online service) |
author_sort |
Schweitzer, Marc Alexander. author. |
title |
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / |
title_short |
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / |
title_full |
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / |
title_fullStr |
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / |
title_full_unstemmed |
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / |
title_sort |
parallel multilevel partition of unity method for elliptic partial differential equations [electronic resource] / |
publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg, |
publishDate |
2003 |
url |
http://dx.doi.org/10.1007/978-3-642-59325-3 |
work_keys_str_mv |
AT schweitzermarcalexanderauthor aparallelmultilevelpartitionofunitymethodforellipticpartialdifferentialequationselectronicresource AT springerlinkonlineservice aparallelmultilevelpartitionofunitymethodforellipticpartialdifferentialequationselectronicresource AT schweitzermarcalexanderauthor parallelmultilevelpartitionofunitymethodforellipticpartialdifferentialequationselectronicresource AT springerlinkonlineservice parallelmultilevelpartitionofunitymethodforellipticpartialdifferentialequationselectronicresource |
_version_ |
1756267570385649664 |