human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "high level implementation of geometric multigrid solvers for finite element problems applications in atmospheric modelling"):
  Abstract: The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated (mixed) finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have in-depth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstraction levels and give the programmer control over details of the preconditioner. We use the composable abstractions of the Firedrake/PyOP2 package to demonstrate the efficiency of this approach for the solution of strongly anisotropic PDEs in atmospheric modelling. The weak formulation of the PDE is expressed in Unified Form Language (UFL) and the lower PyOP2 abstraction layer allows the manual design of computational kernels for a bespoke geometric multigrid preconditioner. We compare the performance of this preconditioner to a single-level method and hypre's BoomerAMG algorithm. The Firedrake/PyOP2 code is inherently parallel and we present a detailed performance analysis for a single node (24 cores) on the ARCHER supercomputer. Our implementation utilises a significant fraction of the available memory bandwidth and shows very good weak scaling on up to 6,144 compute cores.

Includes members:
  Member "firedrake automating the finite element method by composing abstractions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "automatic weak imposition of free slip boundary conditions via nitsche s method application to nonlinear problems in geodynamics")
  Member "an algorithm for the optimization of finite element integration loops":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "automatically harnessing sparse acceleration")
  Member "acceleration of a full scale industrial cfd application with op2":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "data management in industry 4 0 state of the art and open challenges")
  Member "solution of nonlinear stokes equations discretized by high order finite elements on nonconforming and anisotropic meshes with application to ice sheet dynamics":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a numbering algorithm for finite element on extruded meshes which avoids the unstructured mesh penalty")
  Member "cross loop optimization of arithmetic intensity for finite element local assembly":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "devito v3 1 0 an embedded domain specific language for finite differences and geophysical exploration")
  Member "petascale elliptic solvers for anisotropic pdes on gpu clusters":
    also connected through other hyperedges:
      (none)
  Member "massively parallel solvers for elliptic pdes in numerical weather and climate prediction":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "extreme scale multigrid components within petsc")
  Member "unified form language a domain specific language for weak formulations of partial differential equations":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "code generation for generally mapped finite elements")

Question: Please tell me which class the source paper 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.MS(Mathematical Software)