Parallel, fully automatic (hp)-adaptive (2d) finite element package. This paper presents a description of par2Dhp -- a 2D, parallel fully automatic (hp)-adaptive finite element code. The parallel implementation is an extension of the sequential code 2Dhp90, which generates fully automatic (hp)-approximations for solutions of various boundary value problems. The presented work addresses parallelization of each stage of the automatic (hp)-adaptive algorithm, including decomposition of the computational domain, load balancing and data redistribution, a parallel frontal solver, and algorithms for parallel mesh refinement and mesh reconciliation. The application was written in Fortran 90 and MPI, and the load balancing is done through an interface with the Zoltan library. Numerical results are presented for the model L-shape domain problem, and a highly anisotropic heat conduction (battery) problem from Sandia National Laboratories.

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  1. Amor-Martin, Adrian; Garcia-Castillo, Luis E.; Lee, Jin-Fa: Study of accuracy of a non-conformal finite element domain decomposition method (2021)
  2. Smyl, Danny; Liu, Dong: Less is often more: applied inverse problems using (hp)-forward models (2019)
  3. Jomo, John N.; Zander, Nils; Elhaddad, Mohamed; Özcan, Ali; Kollmannsberger, Stefan; Mundani, Ralf-Peter; Rank, Ernst: Parallelization of the multi-level (hp)-adaptive finite cell method (2017)
  4. Zander, Nils; Bog, Tino; Elhaddad, Mohamed; Frischmann, Felix; Kollmannsberger, Stefan; Rank, Ernst: The multi-level (hp)-method for three-dimensional problems: dynamically changing high-order mesh refinement with arbitrary hanging nodes (2016)
  5. Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Schillinger, Dominik; Rank, Ernst: Multi-level (hp)-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes (2015)
  6. Barabasz, Barbara; Gajda-Zagórska, Ewa; Migórski, Stanisław; Paszyński, Maciej; Schaefer, Robert; Smołka, Maciej: A hybrid algorithm for solving inverse problems in elasticity (2014)
  7. Gomez-Revuelto, Ignacio; Garcia-Castillo, Luis E.; Llorente-Romano, Sergio; Pardo, David: A three-dimensional self-adaptive (hp) finite element method for the characterization of waveguide discontinuities (2012)
  8. Pardo, David; Nam, Myung Jin; Torres-Verdín, Carlos; Hoversten, Michael G.; Garay, Iñaki: Simulation of marine controlled source electromagnetic measurements using a parallel Fourier (hp)-finite element method (2011)
  9. Mirjalily, S. A. A.; Ameri, M.: Combination of adaptive grid-embedding and equation adaptation methods for compressible viscous flows (2010)
  10. Paszyński, Maciej; Pardo, David; Torres-Verdín, Carlos; Demkowicz, Leszek; Calo, Victor: A parallel direct solver for the self-adaptive (hp) finite element method (2010)
  11. Matuszyk, Pawel; Paszyński, Maciej: Fully automatic hp adaptive finite element method for the Stokes problem in two dimensions (2008)
  12. Šolín, Pavel; Červený, Jakub; Doležel, Ivo: Arbitrary-level hanging nodes and automatic adaptivity in the (hp)-FEM (2008)
  13. Kurtz, J.; Demkowicz, L.: A fully automatic (hp)-adaptivity for elliptic PDEs in three dimensions (2007)
  14. Paszyński, M.; Demkowicz, L.: Parallel, fully automatic hp -adaptive 3D finite element package (2007) ioport
  15. Vejchodský, Tomáš; Šolín, Pavel; Zítka, Martin: Modular hp-FEM system HERMES and its application to Maxwell’s equations (2007)
  16. Paszyński, M.; Demkowicz, L.: Parallel, fully automatic hp -adaptive 3D finite element package (2006) ioport
  17. Paszyński, M.; Kurtz, J.; Demkowicz, L.: Parallel, fully automatic (hp)-adaptive (2d) finite element package (2006)