The Iterative Solver Template Library

Blatt, Markus; Bastian, Peter

doi:10.1007/978-3-540-75755-9_82

Cited by 84 publications

(78 citation statements)

References 7 publications

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“…• Dune MGS is a geometric multi-grid solver based on the Dune framework [3]. The framework provides algorithms for smoothing and solving Poisson equations on structured grids.…”

Section: Experiments #2: Effort and Accuracymentioning

confidence: 99%

Performance-influence models for highly configurable systems

Siegmund

Grebhahn

Apel

et al. 2015

Proceedings of the 2015 10th Joint Meeting on Foundations of Software Engineering

200

245

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Almost every complex software system today is configurable. While configurability has many benefits, it challenges performance prediction, optimization, and debugging. Often, the influences of individual configuration options on performance are unknown. Worse, configuration options may interact, giving rise to a configuration space of possibly exponential size. Addressing this challenge, we propose an approach that derives a performance-influence model for a given configurable system, describing all relevant influences of configuration options and their interactions. Our approach combines machine-learning and sampling heuristics in a novel way. It improves over standard techniques in that it (1) represents influences of options and their interactions explicitly (which eases debugging), (2) smoothly integrates binary and numeric configuration options for the first time, (3) incorporates domain knowledge, if available (which eases learning and increases accuracy), (4) considers complex constraints among options, and (5) systematically reduces the solution space to a tractable size. A series of experiments demonstrates the feasibility of our approach in terms of the accuracy of the models learned as well as the accuracy of the performance predictions one can make with them.

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“…• Dune MGS is a geometric multi-grid solver based on the Dune framework [3]. The framework provides algorithms for smoothing and solving Poisson equations on structured grids.…”

Section: Experiments #2: Effort and Accuracymentioning

confidence: 99%

Performance-influence models for highly configurable systems

Siegmund

Grebhahn

Apel

et al. 2015

Proceedings of the 2015 10th Joint Meeting on Foundations of Software Engineering

200

245

View full text Add to dashboard Cite

show abstract

“…Observe that the representations (114) and (115) coincide because of the chain and product rules. But for I n 1∶3 , the convergence of the terms in (113) can be obtained with standard tools using (21), (32), (39), (88), (92), (93), and (110). We thus leave these details aside and concentrate on the weak L 1 limit for I n 1∶3 .…”

Section: Convergence In (5)mentioning

confidence: 99%

A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow dichotomy hypothesis

Zhigun

Surulescu

Hunt

2018

Math Methods in App Sciences

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We propose and study a strongly coupled PDE‐ODE‐ODE system modeling cancer cell invasion through a tissue network under the go‐or‐grow hypothesis asserting that cancer cells can either move or proliferate. Hence, our setting features 2 interacting cell populations with their mutual transitions and involves tissue‐dependent degenerate diffusion and haptotaxis for the moving subpopulation. The proliferating cells and the tissue evolution are characterized by way of ODEs for the respective densities. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations in a 2‐dimensional setting. The numerical results recover qualitatively the infiltrative patterns observed histologically and moreover allow to establish a qualitative relationship between the structure of the tissue and the expansion of the tumour, thereby paying heed to its heterogeneity.

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“…We would like to thank Christian Engwer for supplying us with a discontinuous Galerkin discretization code (not using weighted averages) and the restriction operator to the conforming space. Furthermore, we are grateful to the developers of the ‘Distributed and Unified Numerics Environment’ (DUNE), see , for providing their PDE and iterative solver code as open source to the public at http://www.dune-project.org. Without them, this work would not have been possible.…”

Section: Acknowledgementsmentioning

confidence: 99%

Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems

Bastian

Blatt

Scheichl

2012

Numerical Linear Algebra App

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SUMMARY We present a new algebraic multigrid (AMG) algorithm for the solution of linear systems arising from discontinuous Galerkin (DG) discretizations of heterogeneous elliptic problems. The algorithm is based on the idea of subspace corrections, and the first coarse level space is the subspace spanned by continuous linear basis functions. The linear system associated with this space is constructed algebraically using a Galerkin approach with the natural embedding as the prolongation operator. This embedding operator needs to be provided, which means that the approach is not fully algebraic. For the construction of the linear systems on the subsequent coarser levels, non‐smoothed aggregation AMG techniques are used. In a series of numerical experiments, we establish for the first time the efficiency and robustness of an AMG method for various symmetric and non‐symmetric interior penalty DG methods (including the higher‐order cases) on problems with complicated, high contrast jumps in the coefficients. The solver is robust with respect to an increase in the polynomial degree of the DG approximation space (at least up to degree 6), computationally efficient, and affected only mildly by the coefficient jumps and by the mesh size h (i.e., number of iterations = O(log h−1)). Copyright © 2012 John Wiley & Sons, Ltd.

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The Iterative Solver Template Library

Cited by 84 publications

References 7 publications

Performance-influence models for highly configurable systems

Performance-influence models for highly configurable systems

A strongly degenerate diffusion‐haptotaxis model of tumour invasion under the go‐or‐grow dichotomy hypothesis

Algebraic multigrid for discontinuous Galerkin discretizations of heterogeneous elliptic problems

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