MOOSE: A parallel computational framework for coupled systems of nonlinear equations. Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation of nuclear processes. MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at the solution of such systems, is presented. As opposed to traditional data-flow oriented computational frameworks, MOOSE is instead founded on the mathematical principle of Jacobian-free Newton–Krylov (JFNK). Utilizing the mathematical structure present in JFNK, physics expressions are modularized into “Kernels,” allowing for rapid production of new simulation tools. In addition, systems are solved implicitly and fully coupled, employing physics-based preconditioning, which provides great flexibility even with large variance in time scales. A summary of the mathematics, an overview of the structure of MOOSE, and several representative solutions from applications built on the framework are presented.

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  1. Keilegavlen, Eirik; Berge, Runar; Fumagalli, Alessio; Starnoni, Michele; Stefansson, Ivar; Varela, Jhabriel; Berre, Inga: PorePy: an open-source software for simulation of multiphysics processes in fractured porous media (2021)
  2. Koch, Timo; Gläser, Dennis; Weishaupt, Kilian; Ackermann, Sina; Beck, Martin; Becker, Beatrix; Burbulla, Samuel; Class, Holger; Coltman, Edward; Emmert, Simon; Fetzer, Thomas; Grüninger, Christoph; Heck, Katharina; Hommel, Johannes; Kurz, Theresa; Lipp, Melanie; Mohammadi, Farid; Scherrer, Samuel; Schneider, Martin; Seitz, Gabriele; Stadler, Leopold; Utz, Martin; Weinhardt, Felix; Flemisch, Bernd: DuMu(^\textx 3) -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling (2021)
  3. Chen, Xi; Williams, David M.: Versatile mixed methods for the incompressible Navier-Stokes equations (2020)
  4. Favino, Marco; Hunziker, Jürg; Caspari, Eva; Quintal, Beatriz; Holliger, Klaus; Krause, Rolf: Fully-automated adaptive mesh refinement for media embedding complex heterogeneities: application to poroelastic fluid pressure diffusion (2020)
  5. Kim, Tae-Yeon; Jiang, Wen; Lee, Sungmun; Song, Jeong-Hoon; Yeun, Chan Yeob; Park, Eun-Jae: A Nitsche-type variational formulation for the shape deformation of a single component vesicle (2020)
  6. Kopaničáková, Alena; Krause, Rolf: A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture (2020)
  7. Lesueur, Martin; Poulet, Thomas; Veveakis, Manolis: Three-scale multiphysics finite element framework (FE(^3)) modelling fault reactivation (2020)
  8. von Planta, Cyrill; Vogler, Daniel; Chen, Xiaoqing; Nestola, Maria G. C.; Saar, Martin O.; Krause, Rolf: Modelling of hydro-mechanical processes in heterogeneous fracture intersections using a fictitious domain method with variational transfer operators (2020)
  9. Zhang, Shuaifang; Jiang, Wen; Tonks, Michael R.: A new phase field fracture model for brittle materials that accounts for elastic anisotropy (2020)
  10. Chen, Hailong: A comparison study on peridynamic models using irregular non-uniform spatial discretization (2019)
  11. Huang, D. Z.; Persson, P.-O.; Zahr, M. J.: High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit-explicit Runge-Kutta schemes (2019)
  12. Liu, Yingjie; Peco, Christian; Dolbow, John: A fully coupled mixed finite element method for surfactants spreading on thin liquid films (2019)
  13. Timo Koch, Dennis Gläser, Kilian Weishaupt, Sina Ackermann, Martin Beck, Beatrix Becker, Samuel Burbulla, Holger Class, Edward Coltman, Simon Emmert, Thomas Fetzer, Christoph Grüninger, Katharina Heck, Johannes Hommel, Theresa Kurz, Melanie Lipp, Farid Mohammadi, Samuel Scherrer, Martin Schneider, Gabriele Seitz, Leopold Stadler, Martin Utz, Felix Weinhardt, Bernd Flemisch: DuMuX 3 -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling (2019) arXiv
  14. von Planta, Cyrill; Vogler, Daniel; Chen, Xiaoqing; Nestola, Maria G. C.; Saar, Martin O.; Krause, Rolf: Simulation of hydro-mechanically coupled processes in rough rock fractures using an immersed boundary method and variational transfer operators (2019)
  15. Badia, Santiago; Martín, Alberto F.; Principe, Javier: \textttFEMPAR: an object-oriented parallel finite element framework (2018)
  16. Bilgen, Carola; Kopaničáková, Alena; Krause, Rolf; Weinberg, Kerstin: A phase-field approach to conchoidal fracture (2018)
  17. Chang, Justin; Fabien, Maurice S.; Knepley, Matthew G.; Mills, Richard T.: Comparative study of finite element methods using the time-accuracy-size (TAS) spectrum analysis (2018)
  18. Mao, Yunwei; Anand, Lallit: A theory for fracture of polymeric gels (2018)
  19. Timothy J. Truster: DEIP, discontinuous element insertion Program - Mesh generation for interfacial finite element modeling (2018) not zbMATH
  20. Green, David K. E.: Efficient Markov chain Monte Carlo for combined subset simulation and nonlinear finite element analysis (2017)

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