Nonlinear Krylov acceleration applied to a discrete ordinates formulation of the k-eigenvalue problem

Calef, Matthew T.; Fichtl, Erin D.; Warsa, James S.; Berndt, Markus; Carlson, Neil N.

doi:10.1016/j.jcp.2012.12.024

Cited by 45 publications

(27 citation statements)

References 30 publications

(81 reference statements)

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“…We use a two-point flux discretization for both the surface and subsurface equations; this choice, while less accurate than some, is strictly monotonicity-preserving, which is critical for accurate and efficient solution of freezing soil dynamics. A Nonlinear Krylov Acceleration method (Calef et al 2013), modified to include significant globalization including backtracking and physics-based strategies, was used to solve the resulting globally-implicit coupled system of equations.…”

Section: Ats Modelmentioning

confidence: 99%

Modeling the role of preferential snow accumulation in through talik development and hillslope groundwater flow in a transitional permafrost landscape

Jafarov

Coon

Harp

et al. 2018

Environ. Res. Lett.

106

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Through taliks-thawed zones extending through the entire permafrost layer-represent a critical type of heterogeneity that affects water redistribution and heat transport, especially in sloping landscapes. The formation of through taliks as part of the transition from continuous to discontinuous permafrost creates new hydrologic pathways connecting the active layer to sub-permafrost regions, with significant hydrological and biogeochemical consequences. At hilly field sites in the southern Seward Peninsula, AK, patches of deep snow in tall shrubs are associated with higher winter ground temperatures and an anomalously deep active layer. To better understand the thermal-hydrologic controls and consequences of through taliks, we used the coupled surface/subsurface permafrost hydrology model ATS (Advanced Terrestrial Simulator) to simulate through taliks associated with preferentially distributing snow. Scenarios were developed based on an intensively studied hillslope transect on the southern Seward Peninsula, which predominately has taller shrubs midslope and tundra in upslope and downslope areas. The model was forced with detrended meteorological data with snow preferentially distributed at the midslope of the domain to investigate the potential role of vegetation-induced snow trapping in controlling through talik development under conditions typical of the current-day Seward Peninsula. We simulated thermal hydrology and talik development for five permafrost conditions ranging in thickness from 17-45 m. For the three thinnest permafrost configurations, a through talik developed, which allowed water from the seasonally thawed layer into sub-permafrost waters, increasing sub-permafrost groundwater flow. These numerical experiments suggest that in the transition from continuous to discontinuous permafrost, through taliks may appear at locations that preferential trap snow and that the appearance of those through taliks may drive significant changes in permafrost hydrology.

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Section: Ats Modelmentioning

confidence: 99%

Modeling the role of preferential snow accumulation in through talik development and hillslope groundwater flow in a transitional permafrost landscape

Jafarov

Coon

Harp

et al. 2018

Environ. Res. Lett.

106

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“…In choosing coefficients ξ j to give the exact solution if the underlying problem were linear, Anderson acceleration functions somewhat like Newton's method, which can jump di-rectly to the solution in a single iteration when applied to a linear problem. 2 While rigorous theoretical results regarding the convergence rate of Anderson acceleration at finite M have not been derived, practical tests shows that the method achieves convergence rates competitive with other Newton-like methods, which are generally super-linear (Calef et al, 2013;Willert et al, 2014).…”

Section: Anderson Accelerationmentioning

confidence: 99%

VADER: A flexible, robust, open-source code for simulating viscous thin accretion disks

Krumholz

Forbes

2015

Astronomy and Computing

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The evolution of thin axisymmetric viscous accretion disks is a classic problem in astrophysics. While models based on this simplified geometry provide only approximations to the true processes of instability-driven mass and angular momentum transport, their simplicity makes them invaluable tools for both semi-analytic modeling and simulations of long-term evolution where two-or three-dimensional calculations are too computationally costly. Despite the utility of these models, the only publicly-available frameworks for simulating them are rather specialized and non-general. Here we describe a highly flexible, general numerical method for simulating viscous thin disks with arbitrary rotation curves, viscosities, boundary conditions, grid spacings, equations of state, and rates of gain or loss of mass (e.g., through winds) and energy (e.g., through radiation). Our method is based on a conservative, finite-volume, second-order accurate discretization of the equations, which we solve using an unconditionally-stable implicit scheme. We implement Anderson acceleration to speed convergence of the scheme, and show that this leads to factor of ∼ 5 speed gains over non-accelerated methods in realistic problems, though the amount of speedup is highly problem-dependent. We have implemented our method in the new code Viscous Accretion Disk Evolution Resource (VADER), which is freely available for download from https://bitbucket.org/krumholz/vader/ under the terms of the GNU General Public License.

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“…Moreover, for every A, the compatibility inequality is sharp (satisfied as an equality for some x), which characterizes a subordinate matrix norm induced by a compatible vector norm. We shall later encounter compatible vector and matrix norms satisfying (1) - (5) for which (5) may be sharp for some A, but not all A, so the matrix norm is not induced by and subordinate to the vector norm. Finally, we observe the normalization property of a subordinate matrix norm…”

Section: Normsmentioning

confidence: 99%

Comments on “Anderson Acceleration, Mixing and Extrapolation”

Anderson

2018

Numer Algor

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In 1962, during the course of my doctoral dissertation research, I devised a technique for accelerating the convergence of the Picard iteration associated with a fixed point problem, which I called the Extrapolation Algorithm. More recently, versions of this method have been labelled as Anderson Acceleration in the applied mathematics community and Anderson Mixing in the computational quantum mechanics community.

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Nonlinear Krylov acceleration applied to a discrete ordinates formulation of the k-eigenvalue problem

Cited by 45 publications

References 30 publications

Modeling the role of preferential snow accumulation in through talik development and hillslope groundwater flow in a transitional permafrost landscape

Modeling the role of preferential snow accumulation in through talik development and hillslope groundwater flow in a transitional permafrost landscape

VADER: A flexible, robust, open-source code for simulating viscous thin accretion disks

Comments on “Anderson Acceleration, Mixing and Extrapolation”

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