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## Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling (2011)

Citations: | 2 - 1 self |

### Citations

428 |
Domain Decomposition Methods for Partial Differential Equations Series: Numerical Mathematics and Scientific Computation,
- Quarteroni, Valli
- 1999
(Show Context)
Citation Context ...ion [28]. 5. Parallel implementation Parallel computations apply a divide and conquer strategy to solve large-scale problems. In our parallel solvers, we adopted the domain decomposition method (DDM) =-=[9, 45]-=-, i.e., we divide the modeling domain into sub-domains and solve for the unknowns in the subdomains simultaneously on distributed computer processors. The finite element mesh is first partitioned into... |

387 | Centroidal Voronoi tessellations: Applications and algorithms
- Du, Faber, et al.
- 1999
(Show Context)
Citation Context ...esolution triangular grid for the twodimensional domain ΩH that defines the horizontal extent of the ice sheet. For this purpose, we use centroidal Voronoi tessellation (CVT)-based meshing techniques =-=[10, 11, 21]-=-. CVTs are special Voronoi tessellations having the property that the generators of the Voronoi tessellations are also the centroids, with respect to a given density function, of the corresponding Vor... |

267 | A fully asynchronous multifrontal solver using distributed dynamic scheduling:
- Amestoy, Duff, et al.
- 2001
(Show Context)
Citation Context ... products. In recent years, many parallel solvers for large-scale linear systems have become available in the public domain. These include Multifrontal Massively Parallel sparse direct Solver (MUMPS) =-=[3]-=-, SuperLU [29], AZTEC [44], and parallel Algebraic Recursive Multilevel Solvers (pARMS) [30]. Basically, there are two types of parallel iterative linear system solvers based on Krylov methods: the GM... |

240 |
The Physics of Glaciers.
- Paterson
- 1994
(Show Context)
Citation Context ... ui, j + u j,i = 1 2 ∂ ui ∂ x j + ∂ u j ∂ x i . (2.5) The constitutive law for ice connects the viscous stress tensor τ to the strain rate tensor ǫ̇u by the generalized form of Glen’s flow law =-=[38,39]-=- τ = 2ηu,T ǫ̇u or τi j = 2ηu,T ǫ̇i j, (2.6) where ηu,T = 1 2 A−1/nǫ̇(1−n)/ne , (2.7) 362 H. Zhang, L. Ju, M. Gunzburger, T. Ringler and S. Price and ηu,T denotes the temperature and strain rate-depend... |

145 | SuperLU_DIST: A Scalable Distributed-Memory Sparse Direct Solver for Unsymmetric Linear Systems,
- Li, Demmel
- 2003
(Show Context)
Citation Context ...on computing power and memory. Iterative solution techniques based on Krylov subspace methods (as well as preconditioning techniques, such as multi-grid and incomplete LU factorization preconditioner =-=[29]-=-) are commonly used because the Krylov subspace iteration methods require only matrix-vector products. In recent years, many parallel solvers for large-scale linear systems have become available in th... |

63 | Analysis of least-squares finite element methods for the navier-stokes equations,
- Bochev
- 1997
(Show Context)
Citation Context ...ose of the latter over the nodes of the CVDT triangulation Th. The choice we made for the finite element spaces for the velocity and pressure does not satisfy the LBB (or inf-sup) stability condition =-=[14]-=- required for mixed finite element methods. Thus, to circumvent the LBB condition, we discretize the Stokes equation using a penalty method, i.e., we add a penalty term to the variational formulation ... |

56 |
Runoff and mass balance of the Greenland ice sheet: 1958–2003
- Hanna, Huybrechts, et al.
(Show Context)
Citation Context ... Zhang, L. Ju, M. Gunzburger, T. Ringler and S. Price maximum and minimum values of the ice thickness are 3340 m and 5m, respectively. Observational data of the annual average ice surface temperature =-=[15]-=- is also given in Fig. 6. As shown in the right of Fig. 6, the temperature in some marginal areas of the Greenland ice sheet is already above the melting point. Figure 5: The horizontal speed of the i... |

55 | Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients. - Blatter - 1995 |

53 |
Large-scale changes in Greenland outlet glacier dynamics triggered at the terminus.
- Nick, Veili, et al.
- 2009
(Show Context)
Citation Context ...aciers and ice sheets remains an open question. Our approach uses finite element discretizations of the mechanical and thermal components. Based on observations from field and satellite-based studies =-=[5, 34, 35, 37]-=-, another key component is a high-quality, adaptive, variable resolution meshing scheme that can often significantly reduce the computational cost while maintaining comparable solution accuracy relati... |

43 |
A new, highresolution digital elevation model of Greenland fully validated with airborne laser altimeter data.
- Bamber, Ekholm, et al.
- 2001
(Show Context)
Citation Context ...aciers and ice sheets remains an open question. Our approach uses finite element discretizations of the mechanical and thermal components. Based on observations from field and satellite-based studies =-=[5, 34, 35, 37]-=-, another key component is a high-quality, adaptive, variable resolution meshing scheme that can often significantly reduce the computational cost while maintaining comparable solution accuracy relati... |

38 | pARMS: a parallel version of the algebraic recursive multilevel solver
- LI, SAAD, et al.
- 2003
(Show Context)
Citation Context ...e available in the public domain. These include Multifrontal Massively Parallel sparse direct Solver (MUMPS) [3], SuperLU [29], AZTEC [44], and parallel Algebraic Recursive Multilevel Solvers (pARMS) =-=[30]-=-. Basically, there are two types of parallel iterative linear system solvers based on Krylov methods: the GMRES and BiCG stabilized type for nonsymmetric systems and the conjugate gradient type for sy... |

37 | 2007), Ice-sheet contributions to future sea-level change, Philos - Gregory, Huybrechts |

37 | Convergence of a substructuring method with Lagrange multipliers.
- Mandel, Tezaur
- 1996
(Show Context)
Citation Context ...r interfaces, i.e., the degrees of freedom corresponding to the grid points common to more than one subdomain [27,46]. A variety of methods, including Lagrange multiplier-based substructuring methods =-=[32]-=-, preconditioned Krylov subspace iterative methods [4, 20], parallel direct solvers [1], and multi-grid [9, 25] and multi-level [4] solvers, can be used to solve the linear systems introduced in Secti... |

35 |
and others. Benchmark experiments for higher-order and full Stokes ice sheet models (ISMIP-HOM). The Cryosphere,
- Pattyn
- 2008
(Show Context)
Citation Context ...Gunzburger, T. Ringler and S. Price [6–8, 13]. Among the different types of approaches employed, the full three-dimensional Stokes ice sheet model is generally accepted to truly model ice sheet flows =-=[18,28,41,42]-=-. A three-dimensional full-Stokes ice sheet computational model requires the integration of effective gridding strategies, discretization schemes, couplers for data exchange between model components, ... |

30 |
A preconditioner based on domain decomposition for h-p finite element approximation on quasi-uniform meshes.
- Ainsworth
- 1996
(Show Context)
Citation Context ...er problems that can be simultaneously solved on different processors. The sub-domains could be overlapping or non-overlapping, depending on the specific scheme employed. A variety of preconditioners =-=[2]-=- can used to tackle inner interfaces, i.e., the degrees of freedom corresponding to the grid points common to more than one subdomain [27,46]. A variety of methods, including Lagrange multiplier-based... |

22 | Time-step limits for stable solutions of the ice-sheet equation - Hindmarsh, Payne - 1996 |

20 |
Preconditioned iterative methods for Stokes flow problems arising in computational geodynamics
- May, Moresi
- 2008
(Show Context)
Citation Context ...re are two types of parallel iterative linear system solvers based on Krylov methods: the GMRES and BiCG stabilized type for nonsymmetric systems and the conjugate gradient type for symmetric systems =-=[33]-=-. Message Passing Interface (MPI) is used as the parallel environment and we also chose to use the parallel ILU(ǫ̇) preconditioned GMRES solver for solution of the linear systems resulting from our nu... |

18 | Domain decomposition preconditioning in the hierarchical p-version of the finite element method.
- Korneev, Jensen
- 1999
(Show Context)
Citation Context ... on the specific scheme employed. A variety of preconditioners [2] can used to tackle inner interfaces, i.e., the degrees of freedom corresponding to the grid points common to more than one subdomain =-=[27,46]-=-. A variety of methods, including Lagrange multiplier-based substructuring methods [32], preconditioned Krylov subspace iterative methods [4, 20], parallel direct solvers [1], and multi-grid [9, 25] a... |

15 | Advances in studies and applications of centroidal Voronoi tessellations.
- Du, Gunzburger, et al.
- 2010
(Show Context)
Citation Context ...ow water equations [43]; CVT-based mesh generation offers significant advantages, compared to other meshing algorithms, for improving discretization/solution accuracy and controlling local mesh sizes =-=[11,17,21,22,24,43]-=-. This paper reports on progress made towards the development of an efficient, parallel, finite element solver for three-dimensional, full-Stokes ice sheet modeling. The coupled thermo-mechanical proc... |

15 |
The distribution of stress and velocity in glaciers and ice
- Nye
- 1957
(Show Context)
Citation Context ... ui, j + u j,i = 1 2 ∂ ui ∂ x j + ∂ u j ∂ x i . (2.5) The constitutive law for ice connects the viscous stress tensor τ to the strain rate tensor ǫ̇u by the generalized form of Glen’s flow law =-=[38,39]-=- τ = 2ηu,T ǫ̇u or τi j = 2ηu,T ǫ̇i j, (2.6) where ηu,T = 1 2 A−1/nǫ̇(1−n)/ne , (2.7) 362 H. Zhang, L. Ju, M. Gunzburger, T. Ringler and S. Price and ηu,T denotes the temperature and strain rate-depend... |

15 | 2008: A multiresolution method for climate system modeling: Application of spherical centroidal Voronoi tessellations
- Ju, Gunzburger
(Show Context)
Citation Context ...have been widely incorporated into finite volume and finite element approximation schemes for convection-diffusion equations [12, 22], the NavierStokes equations [23], and the shallow water equations =-=[43]-=-; CVT-based mesh generation offers significant advantages, compared to other meshing algorithms, for improving discretization/solution accuracy and controlling local mesh sizes [11,17,21,22,24,43]. Th... |

13 |
Sparse iterative algorithm software for large-scale MIMD machines: An initial discussion and implementation. Concurrency: Practice and Experience
- Shadid, Tuminaro
- 1992
(Show Context)
Citation Context ...s, many parallel solvers for large-scale linear systems have become available in the public domain. These include Multifrontal Massively Parallel sparse direct Solver (MUMPS) [3], SuperLU [29], AZTEC =-=[44]-=-, and parallel Algebraic Recursive Multilevel Solvers (pARMS) [30]. Basically, there are two types of parallel iterative linear system solvers based on Krylov methods: the GMRES and BiCG stabilized ty... |

12 | Finite volume methods on spheres and spherical centroidal Voronoi meshes
- Du, Ju
- 2005
(Show Context)
Citation Context ...ly, centroidal Voronoi tessellation (CVT) based mesh generation techniques have been widely incorporated into finite volume and finite element approximation schemes for convection-diffusion equations =-=[12, 22]-=-, the NavierStokes equations [23], and the shallow water equations [43]; CVT-based mesh generation offers significant advantages, compared to other meshing algorithms, for improving discretization/sol... |

12 |
K.: Sensitivity study of a dynamic thermodynamic sea ice model
- Holland, Mysak, et al.
- 1993
(Show Context)
Citation Context ...e solvers. Finite difference, finite volume, and finite element methods have proven successful for high-resolution computational simulations based on the full-Stokes model with free surface evolution =-=[19,40,42]-=-. However, the applicability of the methods for large-scale, highresolution simulations of realistic glaciers and ice sheets remains an open question. Our approach uses finite element discretizations ... |

12 |
Glacier flow modelling: a comparison of the shallow ice approximation and the full-stokes solution
- Meur, Gagliardini, et al.
- 2004
(Show Context)
Citation Context ...Gunzburger, T. Ringler and S. Price [6–8, 13]. Among the different types of approaches employed, the full three-dimensional Stokes ice sheet model is generally accepted to truly model ice sheet flows =-=[18,28,41,42]-=-. A three-dimensional full-Stokes ice sheet computational model requires the integration of effective gridding strategies, discretization schemes, couplers for data exchange between model components, ... |

11 | A preliminary out-of-core extension of a parallel multifrontal solver
- Agullo, Guermouche, et al.
- 2006
(Show Context)
Citation Context ...re than one subdomain [27,46]. A variety of methods, including Lagrange multiplier-based substructuring methods [32], preconditioned Krylov subspace iterative methods [4, 20], parallel direct solvers =-=[1]-=-, and multi-grid [9, 25] and multi-level [4] solvers, can be used to solve the linear systems introduced in Section 4.2. To decompose the model domain for parallel computing, either edge- or vertex-ba... |

11 |
Multigrid methods in science and engineering,
- DOUGLAS
- 1996
(Show Context)
Citation Context ...ion [28]. 5. Parallel implementation Parallel computations apply a divide and conquer strategy to solve large-scale problems. In our parallel solvers, we adopted the domain decomposition method (DDM) =-=[9, 45]-=-, i.e., we divide the modeling domain into sub-domains and solve for the unknowns in the subdomains simultaneously on distributed computer processors. The finite element mesh is first partitioned into... |

11 |
On the parallelization of multi-grid methods using a non-overlapping domain decomposition data structure
- JUNG
- 1997
(Show Context)
Citation Context ...n [27,46]. A variety of methods, including Lagrange multiplier-based substructuring methods [32], preconditioned Krylov subspace iterative methods [4, 20], parallel direct solvers [1], and multi-grid =-=[9, 25]-=- and multi-level [4] solvers, can be used to solve the linear systems introduced in Section 4.2. To decompose the model domain for parallel computing, either edge- or vertex-based partition methods ca... |

11 | A full-stress, thermomechanical flow band model using the finite volume method - Price, Waddington, et al. - 2007 |

10 | G.: High-resolution regional climate simulations over Iceland using Polar MM5 - Bromwich, Bai, et al. |

10 |
Preconditioned iterative methods on sparse subspaces
- Ito, Toivanen
(Show Context)
Citation Context ...g to the grid points common to more than one subdomain [27,46]. A variety of methods, including Lagrange multiplier-based substructuring methods [32], preconditioned Krylov subspace iterative methods =-=[4, 20]-=-, parallel direct solvers [1], and multi-grid [9, 25] and multi-level [4] solvers, can be used to solve the linear systems introduced in Section 4.2. To decompose the model domain for parallel computi... |

10 | Multi-constraint mesh partitioning for contact/impact computations
- Karypis
- 2003
(Show Context)
Citation Context ... of variables must be updated systematically. In our implementation, the mesh partition is handled by the multi k-way partitioning algorithm (the package “METIS”) in order to obtain good load balance =-=[26]-=-. The partitioned subdomains have one layer of overlapping elements, that are needed for data communication, i.e., interface updates, during the solution process. We have developed a parallel subsyste... |

9 | Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi Delaunay triangulations
- Ju, Gunzburger, et al.
(Show Context)
Citation Context ...ly, centroidal Voronoi tessellation (CVT) based mesh generation techniques have been widely incorporated into finite volume and finite element approximation schemes for convection-diffusion equations =-=[12, 22]-=-, the NavierStokes equations [23], and the shallow water equations [43]; CVT-based mesh generation offers significant advantages, compared to other meshing algorithms, for improving discretization/sol... |

8 | An algebraic multilevel iteration method for finite element matrices
- Axelsson, Larin
- 1997
(Show Context)
Citation Context ...g to the grid points common to more than one subdomain [27,46]. A variety of methods, including Lagrange multiplier-based substructuring methods [32], preconditioned Krylov subspace iterative methods =-=[4, 20]-=-, parallel direct solvers [1], and multi-grid [9, 25] and multi-level [4] solvers, can be used to solve the linear systems introduced in Section 4.2. To decompose the model domain for parallel computi... |

7 | Conforming centroidal Voronoi Delaunay triangulation for quality mesh generation
- Ju
- 2007
(Show Context)
Citation Context ...ow water equations [43]; CVT-based mesh generation offers significant advantages, compared to other meshing algorithms, for improving discretization/solution accuracy and controlling local mesh sizes =-=[11,17,21,22,24,43]-=-. This paper reports on progress made towards the development of an efficient, parallel, finite element solver for three-dimensional, full-Stokes ice sheet modeling. The coupled thermo-mechanical proc... |

6 |
Constrained CVT meshes and a comparison of triangular mesh generators
- NGUYEN, BURKARDT, et al.
- 2009
(Show Context)
Citation Context ...ow water equations [43]; CVT-based mesh generation offers significant advantages, compared to other meshing algorithms, for improving discretization/solution accuracy and controlling local mesh sizes =-=[11,17,21,22,24,43]-=-. This paper reports on progress made towards the development of an efficient, parallel, finite element solver for three-dimensional, full-Stokes ice sheet modeling. The coupled thermo-mechanical proc... |

6 |
A Community Ice Sheet Model for sea level prediction
- Lipscomb, Bindschadler, et al.
- 2009
(Show Context)
Citation Context ...rge numbers of processors, applying the model to realistic ice sheet settings such as Greenland and Antarctica, and incorporating the dynamical core of the model into next-generation ice sheet models =-=[31]-=- such as the Community Ice Sheet Model. Acknowledgments This work was partially supported by the US DOE Office of Science’s Climate Change Prediction Program through DE-FG02-07ER64431, DE-FG02-07ER644... |

6 |
Surface melt area and water balance modeling on the Greenland Ice Sheet 1995e2005
- Mernild, Liston, et al.
- 2008
(Show Context)
Citation Context ...aciers and ice sheets remains an open question. Our approach uses finite element discretizations of the mechanical and thermal components. Based on observations from field and satellite-based studies =-=[5, 34, 35, 37]-=-, another key component is a high-quality, adaptive, variable resolution meshing scheme that can often significantly reduce the computational cost while maintaining comparable solution accuracy relati... |

6 |
A new 3D higher-order thermomechanical ice-sheet model: Basic sensitivity, ice-stream development and ice flow across subglacial lakes.
- Pattyn
- 2003
(Show Context)
Citation Context ...e solvers. Finite difference, finite volume, and finite element methods have proven successful for high-resolution computational simulations based on the full-Stokes model with free surface evolution =-=[19,40,42]-=-. However, the applicability of the methods for large-scale, highresolution simulations of realistic glaciers and ice sheets remains an open question. Our approach uses finite element discretizations ... |

5 |
2011: Voronoi tessellations and their application to climate and global modeling. Numerical Techniques for Global Atmospheric Models
- Ju, Ringler, et al.
(Show Context)
Citation Context |

4 |
Numerical simulations of the steady Navier-Stokes equations using adaptive meshing schemes
- JU, LEE, et al.
(Show Context)
Citation Context ...CVT) based mesh generation techniques have been widely incorporated into finite volume and finite element approximation schemes for convection-diffusion equations [12, 22], the NavierStokes equations =-=[23]-=-, and the shallow water equations [43]; CVT-based mesh generation offers significant advantages, compared to other meshing algorithms, for improving discretization/solution accuracy and controlling lo... |

4 |
Unstructured graph partitioning for sparse linear system solving, Solving Irregularly Structured Problems in Parallel
- MICHEL, PELLEGRINI, et al.
(Show Context)
Citation Context ...rlapping elements, that are needed for data communication, i.e., interface updates, during the solution process. We have developed a parallel subsystem to directly generate unstructured sparse graphs =-=[36]-=- from hybrid finite element meshes that can be separated from the parallel package as a preprocessor. A partitioning of the Greenland CVDT mesh into 16 sub-meshes is shown in Fig. 2. 370 H. Zhang, L. ... |

2 |
A numerical simulation of the sea-ice cover
- Holland, Ingram, et al.
- 1995
(Show Context)
Citation Context ...Gunzburger, T. Ringler and S. Price [6–8, 13]. Among the different types of approaches employed, the full three-dimensional Stokes ice sheet model is generally accepted to truly model ice sheet flows =-=[18,28,41,42]-=-. A three-dimensional full-Stokes ice sheet computational model requires the integration of effective gridding strategies, discretization schemes, couplers for data exchange between model components, ... |

2 |
mass balance modeling for the entire Mittivakkat Glacier
- Mernild, Liston, et al.
(Show Context)
Citation Context |

1 | Climate of the 21st-Century - BENGTSSON - 1994 |

1 | Schur Complement Domain Decomposition Methods
- ZUMBUSCH
- 1996
(Show Context)
Citation Context ... on the specific scheme employed. A variety of preconditioners [2] can used to tackle inner interfaces, i.e., the degrees of freedom corresponding to the grid points common to more than one subdomain =-=[27,46]-=-. A variety of methods, including Lagrange multiplier-based substructuring methods [32], preconditioned Krylov subspace iterative methods [4, 20], parallel direct solvers [1], and multi-grid [9, 25] a... |