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 "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies"):
  Abstract: It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, used for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems. This figure shows the fate of chromium after 180 days using the single-field Galerkin formulation. The white regions indicate the violation of the non-negative constraint.

Includes members:
  Member "flexible scalable mesh and data management using petsc dmplex":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "pcpatch software for the topological construction of multigrid relaxation methods")
  Member "on mesh restrictions to satisfy comparison principles maximum principles and the non negative constraint recent developments and new results":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "unsupervised machine learning based on non negative tensor factorization for analyzing reactive mixing")
  Member "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "unsupervised machine learning based on non negative tensor factorization for analyzing reactive mixing")
  Member "achieving high performance with unified residual evaluation":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "fast matrix free evaluation of discontinuous galerkin finite element operators")
  Member "a numerical methodology for enforcing maximum principles and the non negative constraint for transient diffusion equations":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity")
  Member "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity")
  Member "non negative mixed finite element formulations for a tensorial diffusion equation":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity")
  Member "mesh algorithms for pde with sieve i mesh distribution":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "non conforming mesh refinement for high order 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.NA(Numerical Analysis)