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 "a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity"):
  Abstract: Abstract   Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations, that is, one needs to satisfy discrete maximum principles (DMP). Unfortunately, many of the existing formulations for flow through porous media models do  not  satisfy DMP. This paper presents a robust, scalable numerical formulation based on variational inequalities (VI), to model non-linear flows through heterogeneous, anisotropic porous media without violating DMP. VI is an optimization technique that places bounds on the numerical solutions of partial differential equations. To crystallize the ideas, a modification to Darcy equations by taking into account pressure-dependent viscosity will be discretized using the lowest-order Raviart–Thomas (RT0) and Variational Multi-scale (VMS) finite element formulations. It will be shown that these formulations violate DMP, and, in fact, these violations increase with an increase in anisotropy. It will be shown that the proposed VI-based formulation provides a viable route to enforce DMP. Moreover, it will be shown that the proposed formulation is scalable, and can work with any numerical discretization and weak form. A series of numerical benchmark problems are solved to demonstrate the effects of heterogeneity, anisotropy and non-linearity on DMP violations under the two chosen formulations (RT0 and VMS), and that of non-linearity on solver convergence for the proposed VI-based formulation. Parallel scalability on modern computational platforms will be illustrated through strong-scaling studies, which will prove the efficiency of the proposed formulation in a parallel setting. Algorithmic scalability as the problem size is scaled up will be demonstrated through novel static-scaling studies. The performed static-scaling studies can serve as a guide for users to be able to select an appropriate discretization for a given problem size.

Includes members:
  Member "a performance spectrum for parallel computational frameworks that solve pdes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "composable block solvers for the four field double porosity permeability model")
  Member "firedrake automating the finite element method by composing abstractions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "automatic weak imposition of free slip boundary conditions via nitsche s method application to nonlinear problems in geodynamics")
  Member "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies":
    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 "an algorithm for the optimization of finite element integration loops":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "automatically harnessing sparse acceleration")
  Member "variational inequality approach to enforcing the non negative constraint for advection diffusion equations":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "composable block solvers for the four field double porosity permeability model")
  Member "cross loop optimization of arithmetic intensity for finite element local assembly":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "devito v3 1 0 an embedded domain specific language for finite differences and geophysical exploration")
  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-7 (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-8 (induced by source paper "unsupervised machine learning based on non negative tensor factorization for analyzing reactive mixing")

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.CE(Computational Engineering, Finance, and Science)