human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "massively parallel solvers for elliptic pdes in numerical weather and climate prediction"
  Abstract: The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale atmospheric fluid dynamics. For stability and efficiency reasons several of the operational forecasting centres, in particular the Met Office and the ECMWF in the UK, use semi-implicit semi-Lagrangian time stepping in the dynamical core of the model. The additional burden with this approach is that a three dimensional elliptic partial differential equation (PDE) for the pressure correction has to be solved at every model time step and this often constitutes a significant proportion of the time spent in the dynamical core. To run within tight operational time scales the solver has to be parallelised and there seems to be a (perceived) misconception that elliptic solvers do not scale to large processor counts and hence implicit time stepping can not be used in very high resolution global models. After reviewing several methods for solving the elliptic PDE for the pressure correction and their application in atmospheric models we demonstrate the performance and very good scalability of Krylov subspace solvers and multigrid algorithms for a representative model equation with more than 10 10 unknowns on 65536 cores on HECToR, the UK’s national supercomputer. For this we tested and optimised solvers from two existing numerical libraries (DUNE and hypre) and implemented both a Conjugate Gradient solver and a geometric multigrid algorithm based on a tensor-product approach which exploits the strong vertical anisotropy of the discretised equation. We study both weak and strong scalability and compare the absolute solution times for all methods; in contrast to one-level methods the multigrid solver is robust with respect to parameter variations. Modern forecast models in numerical weather- and climate- prediction (NWP) use the fully compressible nonhydrostatic Navier-Stokes equations to simulate the dynamics of the atmosphere. If the atmospheric fields are advanced forward in time by explicit time stepping, there are severe limitations on the size of the model timestep, which — for the model to remain stable—, must not exceed the ratio of the grid size and velocity of the fastest waves. For a compressible fluid these are acoustic waves with a speed of several hundred metres per second at ground level. Even if the vertical propagation of sound waves can be dealt with, horizontal grid resolutions are likely to be reduced to a few kilometres in the future, severely limiting the model time step. In contrast, implicit time stepping allows to run the model with larger time steps without compromising its stability and without distorting the large scale flow close to geostrophic balance. However, this requires the solution of an elliptic partial differential equation (PDE) for the pressure correction at every time step. In a non-hydrostatic model this equation has to be solved in three dimensions, i.e. on a spherical shell representing the earth’s atmosphere.

Connected through hyperedge HE-1 (induced by source paper "high level implementation of geometric multigrid solvers for finite element problems applications in atmospheric modelling"):
  with members:
    - "firedrake automating the finite element method by composing abstractions"
    - "an algorithm for the optimization of finite element integration loops"
    - "acceleration of a full scale industrial cfd application with op2"
    - "solution of nonlinear stokes equations discretized by high order finite elements on nonconforming and anisotropic meshes with application to ice sheet dynamics"
    - "cross loop optimization of arithmetic intensity for finite element local assembly"
    - "petascale elliptic solvers for anisotropic pdes on gpu clusters"
    - "unified form language a domain specific language for weak formulations of partial differential equations"
    - "dolfin automated finite element computing"

Connected through hyperedge HE-2 (induced by source paper "extreme scale multigrid components within petsc"):
  with members:
    - "solution of nonlinear stokes equations discretized by high order finite elements on nonconforming and anisotropic meshes with application to ice sheet dynamics"

Connected through hyperedge HE-3 (induced by source paper "evaluating the impact of sdc on the gmres iterative solver"):
  with members:
    - "hard data on soft errors a large scale assessment of real world error rates in gpgpu"

Connected through hyperedge HE-4 (induced by source paper "petascale elliptic solvers for anisotropic pdes on gpu clusters"):
  with members:
    - "matrix free gpu implementation of a preconditioned conjugate gradient solver for anisotropic elliptic pdes"

Question: Please tell me which class the center node belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.DC(Distributed, Parallel, and Cluster Computing)