The Resource A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, by Marc Alexander Schweitzer, (electronic resource)

A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, by Marc Alexander Schweitzer, (electronic resource)

Label
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations
Title
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations
Statement of responsibility
by Marc Alexander Schweitzer
Creator
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
I9W
http://library.link/vocab/creatorName
Schweitzer, Marc Alexander
Dewey number
518
Index
no index present
LC call number
QA71-90
Literary form
non fiction
Nature of contents
encyclopedias
Series statement
Lecture Notes in Computational Science and Engineering, 1439-7358
Series volume
29
http://library.link/vocab/subjectName
  • Mathematics
  • Differential equations, Partial
  • Computer science
  • Engineering mathematics
  • Computer science
  • Differential equations, Partial
  • Engineering mathematics
  • Mathematics
Label
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, by Marc Alexander Schweitzer, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-642-59325-3
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [183]-191) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Partition of Unity Method: Construction of a Partition of Unity Space; Properties; Basic Convergence Theory -- Treatment of Elliptic Equations: Galerkin Discretization; Boundary Conditions; Numerical Results -- Multilevel Solution of the Resulting Linear System: Multilevel Iterative Solvers; Multilevel Partition of Unity Method; Numerical Results -- Tree Partition of Unity Method: Single Level Cover Construction; Construction of a Sequence of PUM spaces; Numerical Results.-Parallelization and Implementational Details: Parallel Data Structures; Parallel Tree Partition of Unity Method; Numerical Results -- Concluding Remarks: Treatment of Other Types of Equations: Parabolic Equations; Hyperbolic Equations; Transformation of Keys; Color Plates -- References -- Index
Dimensions
unknown
Extent
1 online resource (V, 194 pages).
Form of item
online
Isbn
9783540003519
Isbn Type
(pbk. : alk. paper)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
  • (OCoLC)840292681
  • (OCoLC)ocn840292681
Label
A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations, by Marc Alexander Schweitzer, (electronic resource)
Link
http://dx.doi.org/10.1007/978-3-642-59325-3
Publication
Bibliography note
Includes bibliographical references (p. [183]-191) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Introduction -- Partition of Unity Method: Construction of a Partition of Unity Space; Properties; Basic Convergence Theory -- Treatment of Elliptic Equations: Galerkin Discretization; Boundary Conditions; Numerical Results -- Multilevel Solution of the Resulting Linear System: Multilevel Iterative Solvers; Multilevel Partition of Unity Method; Numerical Results -- Tree Partition of Unity Method: Single Level Cover Construction; Construction of a Sequence of PUM spaces; Numerical Results.-Parallelization and Implementational Details: Parallel Data Structures; Parallel Tree Partition of Unity Method; Numerical Results -- Concluding Remarks: Treatment of Other Types of Equations: Parabolic Equations; Hyperbolic Equations; Transformation of Keys; Color Plates -- References -- Index
Dimensions
unknown
Extent
1 online resource (V, 194 pages).
Form of item
online
Isbn
9783540003519
Isbn Type
(pbk. : alk. paper)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Specific material designation
remote
System control number
  • (OCoLC)840292681
  • (OCoLC)ocn840292681

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