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: "a numerical methodology for enforcing maximum principles and the non negative constraint for transient diffusion equations"
  Abstract: Transient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations. It is well-known that, under certain assumptions on the input data, these equations satisfy important mathematical properties like maximum principles and the non-negative constraint, which have implications in mathematical modeling. However, existing numerical formulations for these types of equations do not, in general, satisfy maximum principles and the non-negative constraint. In this paper, we present a methodology for enforcing maximum principles and the non-negative constraint for transient anisotropic diffusion equation. The method of horizontal lines (also known as the Rothe method) is applied in which the time is discretized first. This results in solving steady anisotropic diffusion equation with decay equation at every discrete time level. The proposed methodology for transient anisotropic diffusion equation will satisfy maximum principles and the non-negative constraint on general computational grids, and with no additional restrictions on the time step. We illustrate the performance and accuracy of the proposed formulation using representative numerical examples. We also perform numerical convergence of the proposed methodology. For comparison, we also present the results from the standard single-field semi-discrete formulation and the results from a popular software package, which all will violate maximum principles and the non-negative constraint.

Connected through hyperedge HE-1 (induced by source paper "a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity"):
  with members:
    - "a performance spectrum for parallel computational frameworks that solve pdes"
    - "firedrake automating the finite element method by composing abstractions"
    - "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies"
    - "an algorithm for the optimization of finite element integration loops"
    - "variational inequality approach to enforcing the non negative constraint for advection diffusion equations"
    - "cross loop optimization of arithmetic intensity for finite element local assembly"
    - "on mesh restrictions to satisfy comparison principles maximum principles and the non negative constraint recent developments and new results"
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"

Connected through hyperedge HE-2 (induced by source paper "variational inequality approach to enforcing the non negative constraint for advection diffusion equations"):
  with members:
    - "firedrake automating the finite element method by composing abstractions"
    - "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies"
    - "an algorithm for the optimization of finite element integration loops"
    - "a parallel edge orientation algorithm for quadrilateral meshes"
    - "a structure exploiting numbering algorithm for finite elements on extruded meshes and its performance evaluation in firedrake"
    - "cross loop optimization of arithmetic intensity for finite element local assembly"
    - "on mesh restrictions to satisfy comparison principles maximum principles and the non negative constraint recent developments and new results"
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"

Connected through hyperedge HE-3 (induced by source paper "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies"):
  with members:
    - "flexible scalable mesh and data management using petsc dmplex"
    - "on mesh restrictions to satisfy comparison principles maximum principles and the non negative constraint recent developments and new results"
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"
    - "achieving high performance with unified residual evaluation"
    - "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"
    - "mesh algorithms for pde with sieve i mesh distribution"

Connected through hyperedge HE-4 (induced by source paper "mechanics based solution verification for porous media models"):
  with members:
    - "a stabilized mixed formulation for unsteady brinkman equation based on the method of horizontal lines"
    - "a numerical study of fluids with pressure dependent viscosity flowing through a rigid porous medium"
    - "discussions on driven cavity flow"

Connected through hyperedge HE-5 (induced by source paper "do current lattice boltzmann methods for diffusion and advection diffusion equations respect maximum principle and the non negative constraint"):
  with members:
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"

Connected through hyperedge HE-6 (induced by source paper "on mesh restrictions to satisfy comparison principles maximum principles and the non negative constraint recent developments and new results"):
  with members:
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"
    - "a mixed formulation for a modification to darcy equation based on picard linearization and numerical solutions to large scale realistic problems"
    - "a framework for coupled deformation diffusion analysis with application to degradation healing"
    - "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
    - "well centered triangulation"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"

Connected through hyperedge HE-7 (induced by source paper "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"):
  with members:
    - "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
    - "on the performance of high order finite elements with respect to maximum principles and the non negative constraint for diffusion type equations"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"

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.NA(Numerical Analysis)