FiPy: A Finite Volume PDE Solver Using Python. FiPy is an object oriented, partial differential equation (PDE) solver, written in Python, based on a standard finite volume (FV) approach. The framework has been developed in the Materials Science and Engineering Division (MSED) and Center for Theoretical and Computational Materials Science (CTCMS), in the Material Measurement Laboratory (MML) at the National Institute of Standards and Technology (NIST). The solution of coupled sets of PDEs is ubiquitous to the numerical simulation of science problems. Numerous PDE solvers exist, using a variety of languages and numerical approaches. Many are proprietary, expensive and difficult to customize. As a result, scientists spend considerable resources repeatedly developing limited tools for specific problems. Our approach, combining the FV method and Python, provides a tool that is extensible, powerful and freely available. A significant advantage to Python is the existing suite of tools for array calculations, sparse matrices and data rendering. The FiPy framework includes terms for transient diffusion, convection and standard sources, enabling the solution of arbitrary combinations of coupled elliptic, hyperbolic and parabolic PDEs. Currently implemented models include phase field [BoettingerReview:2002] [ChenReview:2002] [McFaddenReview:2002] treatments of polycrystalline, dendritic, and electrochemical phase transformations as well as a level set treatment of the electrodeposition process [NIST:damascene:2001].

References in zbMATH (referenced in 22 articles )

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  1. Higa, Kenneth; Battaglia, Vincent S.; Srinivasan, Venkat: PyGDH: Python Grid Discretization Helper (2021) not zbMATH
  2. Kuhlman, Kristopher L.; Malama, Bwalya: Uncoupling electrokinetic flow solutions (2021)
  3. Schiano Di Cola, Vincenzo; Cuomo, Salvatore; Severino, Gerardo: Remarks on the numerical approximation of Dirac delta functions (2021)
  4. Zhou, Xu-Hui; Han, Jiequn; Xiao, Heng: Learning nonlocal constitutive models with neural networks (2021)
  5. Boso, Francesca; Tartakovsky, Daniel M.: Data-informed method of distributions for hyperbolic conservation laws (2020)
  6. Karumuri, Sharmila; Tripathy, Rohit; Bilionis, Ilias; Panchal, Jitesh: Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2020)
  7. Aceto, L.; Bertaccini, D.; Durastante, F.; Novati, P.: Rational Krylov methods for functions of matrices with applications to fractional partial differential equations (2019)
  8. Johansson, Robert: Numerical Python. Scientific computing and data science applications with Numpy, SciPy and Matplotlib (2019)
  9. Vega Reyes, Francisco; Puglisi, Andrea; Pontuale, Giorgio; Gnoli, Andrea: Inherent thermal convection in a granular gas inside a box under a gravity field (2019)
  10. Wheeler, D., Keller, T., DeWitt, S.J., Jokisaari, A.M., Schwen, D., Guyer, J.E., Aagesen, L.K., Heinonen, O.G., Tonks, M.R., Voorhees, P.W., Warren, J.A: PFHub: The Phase-Field Community Hub (2019) not zbMATH
  11. Latif, Majid jun.; May, Elebeoba E.: A multiscale agent-based model for the investigation of E. coli K12 metabolic response during biofilm formation (2018)
  12. Lin, Jian-Jhong; Yang, Ting-Hui: Traveling wave solutions for a diffusive three-species intraguild predation model (2018)
  13. Tripathy, Rohit K.; Bilionis, Ilias: Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification (2018)
  14. De La Cruz, Luis M.; Ramos, Eduardo: General template units for the finite volume method in box-shaped domains (2016)
  15. Kelleher, Jerome; Etheridge, A. M.; VĂ©ber, A.; Barton, N. H.: Spread of pedigree versus genetic ancestry in spatially distributed populations (2016)
  16. Goessens, T.; Malengier, B.; Constales, D.; De Staelen, R. H.: A volume averaging and overlapping domain decomposition technique to model mass transfer in textiles (2015)
  17. Kuehn, Christian: Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs (2015)
  18. Lin, Jian-Jhong; Wang, Weiming; Zhao, Caidi; Yang, Ting-Hui: Global dynamics and traveling wave solutions of two predators-one prey models (2015)
  19. Simon, Cory M.; Hepburn, Iain; Chen, Weiliang; De Schutter, Erik: The role of dendritic spine morphology in the compartmentalization and delivery of surface receptors (2014)
  20. Goessens, Tineke; Malengier, Benny; Li, Pei; De Staelen, Rob H.: Diffusion of active ingredients in textiles (2013)

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