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 "variational inequality approach to enforcing the non negative constraint for advection diffusion equations"):
  Abstract: Abstract   Predictive simulations are crucial for the success of many subsurface applications, and it is highly desirable to obtain accurate non-negative solutions for transport equations in these numerical simulations. To this end, optimization-based methodologies based on quadratic programming (QP) have been shown to be a viable approach to ensuring discrete maximum principles and the non-negative constraint for anisotropic diffusion equations. In this paper, we propose a computational framework based on the variational inequality (VI) which can also be used to enforce important mathematical properties (e.g., maximum principles) and physical constraints (e.g., the non-negative constraint). We demonstrate that this framework is not only applicable to diffusion equations but also to non-symmetric advection–diffusion equations. An attractive feature of the proposed framework is that it works with any weak formulation for the advection–diffusion equations, including single-field formulations, which are computationally attractive. A particular emphasis is placed on the parallel and algorithmic performance of the VI approach across large-scale and heterogeneous problems. It is also shown that QP and VI are equivalent under certain conditions. State-of-the-art QP and VI solvers available from the PETSc library are used on a variety of steady-state 2D and 3D benchmarks, and a comparative study on the scalability between the QP and VI solvers is presented. We then extend the proposed framework to transient problems by simulating the miscible displacement of fluids in a heterogeneous porous medium and illustrate the importance of enforcing maximum principles for these types of coupled problems. Our numerical experiments indicate that VIs are indeed a viable approach for enforcing the maximum principles and the non-negative constraint in a large-scale computing environment. Also provided are Firedrake project files as well as a discussion on the computer implementation to help facilitate readers in understanding the proposed framework.

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 "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies":
    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 "an algorithm for the optimization of finite element integration loops":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "automatically harnessing sparse acceleration")
  Member "a parallel edge orientation algorithm for quadrilateral meshes":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "composable block solvers for the four field double porosity permeability model")
  Member "a structure exploiting numbering algorithm for finite elements on extruded meshes and its performance evaluation in firedrake":
    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)