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The Iterative Solver Template Library

The Iterative Solver Template Library,10.1007/978-3-540-75755-9_82,Markus Blatt,Peter Bastian

The Iterative Solver Template Library   (Citations: 14)
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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. 666-675, 2006
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    • ...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 Dedneret al. A generic interface for parallel and adaptive discretization schemes: ...

    • ...Starting from zero, we solve the problem using a conjugate-gradient algorithm preconditioned by a V (4,4)-cycle of the algebraic multigrid algorithm supplied with the dune-istl module [7]...

    Carsten Gräseret al. The dune-subgrid module and some applications

    • ...Release 1.0 includes the core modules dune-common (foundation classes), dune-grid (grid interface and implementations), and dune-istl (iterative solver template library), [6, 7]. The supplementary module dune-grid-howto 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 Bastianet al. A generic grid interface for parallel and adaptive scientific computin...

    • ...However, since we only tested one implementation of aggregation-based 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 Scheichlet al. Additive Schwarz with aggregation-based coarsening for elliptic proble...

    • ...In order to access the different linear solver packages: UMFPACK [17, 18], DUNE-ISTL [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 – DUNE-ISTL is a DUNE module [7, 12], which provides C++ programmed iterative solvers of linear systems stemming from finite element discretizations...

    Robert Eymardet al. 3D Benchmark on Discretization Schemes for Anisotropic Diffusion Probl...

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