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Rights Holder and Contact
Lawrence Livermore National Laboratory
Description
These data represent inputs and solutions to Darcy flow, convection-diffusion, and Poisson problems over 2D square domains. Scripts to generate the datasets are included. Convection-Diffusion and Poisson Dataset These two datasets contain 10,000 steady-state convection-diffusion and pure diffusion problems, respectively, on the 2-D unit square. The problems were discretized by finite element methods (FEM) using [1,2,4]. The input data include the (convection-) diffusion coefficients, mesh point coordinates and heat source (the right-hand sides of the equations). The target data are the numerical solutions obtained by using [3] and the flux of the heat. * [1] FEniCS open source PDE solver https://fenicsproject.org/ * [2] DOLFIN C++/Python interface of FEniCS https://pypi.org/project/DOLFIN/ * [3] Numpy open-source Python library https://numpy.org/ * [4] Sympy open-source Python library https://www.sympy.org/en/index.html Darcy Flow Data This dataset contains finite element solutions of the Darcy Flow equation. Numerical simulations were performed using tools developed in ParELAG[4], a parallel C++ library for performing numerical upscaling of finite element discretizations and AMG techniques, and ParELAGMC [5], a parallel element agglomeration MLMC library. These libraries use MFEM [3] to generate the fine grid finite element discretization and HYPRE [2] to handle massively parallel linear algebra. * [1] GLVis: Opengl finite element visualization tool. glvis.org. * [2] HYPRE: High performance preconditioners. http://www.llnl.gov/CASC/hypre/. * [3] MFEM: Modular finite element methods library. mfem.org. * [4] ParELAG: Element-agglomeration algebraic multigrid and upscaling library, version 2.0. http://github.com/LLNL/parelag, 2015. * [5] ParELAGMC: Parallel element agglomeration multilevel Monte Carlo library. http://github.com/LLNL/parelagmc, 2018. This work was produced under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and was supported by the LLNL-LDRD program under Project No. 19-ERD-019. Research Data Curation Program, UC San Diego, La Jolla, 92093-0175 (https://lib.ucsd.edu/rdcp) Ponce, Colin; Li, Ruipeng; Mao, Christina; Fairbanks, Hilary (2022). Partial Differential Equations (PDE) and Solutions: Darcy Flow, Convection-Diffusion, Poisson Problems. In Lawrence Livermore National Laboratory (LLNL) Open Data Initiative. UC San Diego Library Digital Collections. https://doi.org/10.6075/J0HM58MK
Type
dataset
Identifier
ark:/20775/bb1852369g
Language
No linguistic content
Subject
Poission problem Convection-diffusion problem Partial differential equation Machine learning Numerical problem Finite element method Multilevel Neural Network (MTNN) Darcy Flow problem
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