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of 30
pro vyhledávání: '"Krzysik, Oliver A."'
Graph Neural Networks (GNNs) have established themselves as the preferred methodology in a multitude of domains, ranging from computer vision to computational biology, especially in contexts where data inherently conform to graph structures. While ma
Externí odkaz:
http://arxiv.org/abs/2404.03081
Autor:
Ali, Ahsan, Brannick, James, Kahl, Karsten, Krzysik, Oliver A., Schroder, Jacob B., Southworth, Ben S.
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric setting,
Externí odkaz:
http://arxiv.org/abs/2401.11146
Anderson acceleration (AA) is widely used for accelerating the convergence of an underlying fixed-point iteration $\bm{x}_{k+1} = \bm{q}( \bm{x}_{k} )$, $k = 0, 1, \ldots$, with $\bm{x}_k \in \mathbb{R}^n$, $\bm{q} \colon \mathbb{R}^n \to \mathbb{R}^
Externí odkaz:
http://arxiv.org/abs/2312.04776
Autor:
Ali, Ahsan, Brannick, James, Kahl, Karsten, Krzysik, Oliver A., Schroder, Jacob B., Southworth, Ben S.
Publikováno v:
SIAM J. SCI. COMPUT. 2024 Vol. 0, No. 0, pp. S96-S122
This paper focuses on developing a reduction-based algebraic multigrid method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduct
Externí odkaz:
http://arxiv.org/abs/2307.00229
Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \in \mathbb{R}^n$, but little is known about how to quantify the convergence acceleration provided by AA. As a roadwa
Externí odkaz:
http://arxiv.org/abs/2109.14181
Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solv
Externí odkaz:
http://arxiv.org/abs/2101.01776
Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving
Externí odkaz:
http://arxiv.org/abs/2101.00512
Autor:
De Sterck, Hans, Falgout, Robert D., Friedhoff, Stephanie, Krzysik, Oliver A., MacLachlan, Scott P.
Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent PDEs in modern high-performance computing environments. While these techniques
Externí odkaz:
http://arxiv.org/abs/1910.03726
We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a better understanding of the convergence behaviour of these algorithms f
Externí odkaz:
http://arxiv.org/abs/1902.07757
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