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Keywords
(8)
Finite Element
Generic Programming
Iterative Solver
Linear System
Numerical Solution
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Sparse Linear System
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(1)
On the Generic Parallelisation of Iterative Solvers for the Finite Element Method
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The Iterative Solver Template Library
The Iterative Solver Template Library,10.1007/9783540757559_82,Markus Blatt,Peter Bastian
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The Iterative Solver Template Library
(
Citations: 14
)
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Markus Blatt
,
Peter Bastian
The
numerical solution
of partial differential equations fre quently requires the solution of large and sparse linear systems. Using
generic programming
techniques like in C++ one can create solver li braries that allow efficient realization of "fine grained interfaces", i. e. with functions consisting only of a few lines, like access to individual matrix entries. This prevents code replication and allows programmers to work more efficiently. In this paper we present the "Iterative Solver Template Library" (ISTL) which is part of the "Distributed and Unified Numerics Environment" (DUNE). It applies
generic programming
in C++ to the domain of iter ative solvers of linear systems stemming from
finite element
discretiza tions. Those discretizations exhibit a lot of structure. Our matrix and vector interface supports a block recursive structure. I. E. each
sparse matrix
entry can be a sparse or a small dense matrix itself. Based on this interface we present efficient solvers that use the recursive block structure via template metaprogramming.
Conference:
Workshop on Applied Parallel Computing  PARA
, pp. 666675, 2006
DOI:
10.1007/9783540757559_82
Cumulative
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(
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)
(
www.springerlink.com
)
(
www.informatik.unitrier.de
)
(
www.duneproject.org
)
(
dx.doi.org
)
(
elib.unistuttgart.de
)
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Citation Context
(10)
...Furthermore, Dune Fem provides inverse operators based on the linear solvers and preconditioners (e.g., SSOR and ILU(n)) from Dune Istl (see [
7
])...
Andreas Dedner
,
et al.
A generic interface for parallel and adaptive discretization schemes: ...
...Starting from zero, we solve the problem using a conjugategradient algorithm preconditioned by a V (4,4)cycle of the algebraic multigrid algorithm supplied with the duneistl module [
7
]...
Carsten Gräser
,
et al.
The dunesubgrid module and some applications
...Release 1.0 includes the core modules dunecommon (foundation classes), dunegrid (grid interface and implementations), and duneistl (iterative solver template library), [
6
, 7]. The supplementary module dunegridhowto serves as an introduction to the grid interface...
...The same techniques are used in the Iterative Solver Template Library [
6
], which is also part of DUNE...
Peter Bastian
,
et al.
A generic grid interface for parallel and adaptive scientific computin...
...However, since we only tested one implementation of aggregationbased AMG due to Bastian [2]–[
4
], it remains to be seen whether different smoothers (such as those employed in the ML library [12]) might lead to a multigrid method based on aggregation that is robust on our test problems...
...To put this performance in perspective we compare ADOUG with an aggregationtype AMG preconditioner by Bastian [2], [3], [
4
] (denoted AAMG below) that uses a similar aggregation algorithm (without smoothing) and the same criterion for strong connections as our code, i.e., (24) with ε = 2 . The average coarsening rate inAAMG is...
Robert Scheichl
,
et al.
Additive Schwarz with aggregationbased coarsening for elliptic proble...
...In order to access the different linear solver packages: UMFPACK [17, 18], DUNEISTL [7,
12
], and PETSc [4, 5], all participants were asked to store their resulting linear systems for each test/mesh using a Compressed Row Storage (CRS)...
...2 The Iterative Solver Template Library – DUNEISTL is a DUNE module [7,
12
], which provides C++ programmed iterative solvers of linear systems stemming from finite element discretizations...
Robert Eymard
,
et al.
3D Benchmark on Discretization Schemes for Anisotropic Diffusion Probl...
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Citations
(14)
A generic interface for parallel and adaptive discretization schemes: abstraction principles and the DuneFem module
(
Citations: 2
)
Andreas Dedner
,
Robert Klöfkorn
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Martin Nolte
,
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The dunesubgrid module and some applications
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A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE
(
Citations: 24
)
Peter Bastian
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Markus Blatt
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Andreas Dedner
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Christian Engwer
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Robert Klöfkorn
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Markus Ohlberger
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Oliver Sander
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Additive Schwarz with aggregationbased coarsening for elliptic problems with highly variable coefficients
(
Citations: 22
)
Robert Scheichl
,
Eero Vainikko
Journal:
Computing
, vol. 80, no. 4, pp. 319343, 2007