A Multigrid Tutorial, Second Edition

Briggs, William L.; Henson, Van Emden; McCormick, Steve

doi:10.1137/1.9780898719505

Cited by 1,877 publications

(2,380 citation statements)

References 0 publications

Supporting

Mentioning

2,273

Contrasting

Unclassified

Order By: Relevance

“…The SSA is sufficiently well conditioned for this solver to converge consistently. For the BP, the conditioning is not as good and we have to switch to a preconditioning based on the Multigrid Algebraic method [Briggs et al, 2000]. This solver converges consistently for this type of model.…”

Section: Solvers and Performancementioning

confidence: 99%

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

DeVries

Primeau

2011

Journal of Physical Oceanography

180

202

View full text Add to dashboard Cite

[1] Ice flow models used to project the mass balance of ice sheets in Greenland and Antarctica usually rely on the Shallow Ice Approximation (SIA) and the Shallow-Shelf Approximation (SSA), sometimes combined into so-called "hybrid" models. Such models, while computationally efficient, are based on a simplified set of physical assumptions about the mechanical regime of the ice flow, which does not uniformly apply everywhere on the ice sheet/ice shelf system, especially near grounding lines, where rapid changes are taking place at present. Here, we present a new thermomechanical finite element model of ice flow named ISSM (Ice Sheet System Model) that includes higher-order stresses, high spatial resolution capability and data assimilation techniques to better capture ice dynamics and produce realistic simulations of ice sheet flow at the continental scale. ISSM includes several approximations of the momentum balance equations, ranging from the two-dimensional SSA to the three-dimensional full-Stokes formulation. It also relies on a massively parallelized architecture and state-of-the-art scalable tools. ISSM employs data assimilation techniques, at all levels of approximation of the momentum balance equations, to infer basal drag at the ice-bed interface from satellite radar interferometry-derived observations of ice motion. Following a validation of ISSM with standard benchmarks, we present a demonstration of its capability in the case of the Greenland Ice Sheet. We show ISSM is able to simulate the ice flow of an entire ice sheet realistically at a high spatial resolution, with higher-order physics, thereby providing a pathway for improving projections of ice sheet evolution in a warming climate.Citation: Larour, E., H. Seroussi, M. Morlighem, and E. Rignot (2012), Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM),

show abstract

Section: Solvers and Performancementioning

confidence: 99%

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

DeVries

Primeau

2011

Journal of Physical Oceanography

180

202

View full text Add to dashboard Cite

show abstract

“…The basic idea behind such multilevel methods for solving a linear system Au = f is the recursive application of a simple two-level method consisting of "Smoothing -Restriction -Solution -Prolongation" steps [14,25]. Having access to a hierarchy of meshes can be leveraged to build fast solvers for partial differential equations (PDEs) posed in the volumetric mesh around the biological structure, or posed on the surface mesh (cf.…”

Section: Multilevel Mesh Generation For Multigrid-based Solversmentioning

confidence: 99%

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

Holst

McCammon

2008

Journal of Molecular Graphics and Modelling

105

122

View full text Add to dashboard Cite

We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvment of meshes in a broad range of applications.

show abstract

“…27 Note that even if ρ ext may not correspond to a neutral charge, the sum ρ ext + ρ, where ρ is the charge density of the QM part, is charge neutral. Thus, one can solve Eq.…”

Section: Methodsmentioning

confidence: 99%

Quantitative Assessment of Electrostatic Embedding in Density Functional Theory Calculations of Biomolecular Systems

Fattebert

Law

Bennion

et al. 2009

J. Chem. Theory Comput.

View full text Add to dashboard Cite

We evaluate the accuracy of density functional theory quantum calculations of biomolecular subsystems using a simple electrostatic embedding scheme. Our scheme is based on dividing the system of interest into a primary and secondary subsystem. A finite difference discretization of the Kohn-Sham equations is used for the primary subsystem, while its electrostatic environment is modeled with a simple one-electron potential. Force-field atomic partial charges are used to generate smeared Gaussian charge densities and to model the secondary subsystem. We illustrate the utility of this approach with calculations of truncated dipeptide chains. We analyze quantitatively the accuracy of this approach by calculating atomic forces and comparing results with full QM calculations. The impact of the choice made in terminating dangling bonds at the frontier of the QM region is also investigated.

show abstract

A Multigrid Tutorial, Second Edition

Cited by 1,877 publications

References 0 publications

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

Dynamically and Observationally Constrained Estimates of Water-Mass Distributions and Ages in the Global Ocean

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

Quantitative Assessment of Electrostatic Embedding in Density Functional Theory Calculations of Biomolecular Systems

Contact Info

Product

Resources

About