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paper.bib
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@article{corrado:2022,
title={An Adaptive Anisotropic hp-Refinement Algorithm for the 2D {M}axwell Eigenvalue Problem},
author={Corrado, Jeremiah and Harmon, Jake and Notaros, Branislav},
year={2022},
month={Apr},
url={https://www.techrxiv.org/articles/preprint/An_Adaptive_Anisotropic_hp-Refinement_Algorithm_for_the_2D_Maxwell_Eigenvalue_Problem/19636770},
doi={10.36227/techrxiv.19636770.v1}
}
@article{corrado:2021,
title={A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM},
url={https://www.techrxiv.org/articles/preprint/A_Refinement-by-Superposition_Approach_to_Fully_Anisotropic_hp-Refinement_for_Improved_Efficiency_in_CEM/16695163/1}, DOI={10.36227/techrxiv.16695163.v1},
abstractNote={We present an application of fully anisotropic hp-adaptivity over quadrilateral meshes for H(curl)-conforming discretizations in Computational Electromagnetics (CEM). Traditionally, anisotropic h-adaptivity has been difficult to implement under the constraints of the Continuous Galerkin Formulation; however, Refinement-by-Superposition (RBS) facilitates anisotropic mesh adaptivity with great ease. We present a general discussion of the theoretical considerations involved with implementing fully anisotropic hp-refinement, as well as an in-depth discussion of the practical considerations for 2-D FEM. Moreover, to demonstrate the benefits of both anisotropic h- and p-refinement, we study the 2-D Maxwell eigenvalue problem as a test case. The numerical results indicate that fully anisotropic refinement can provide significant gains in efficiency, even in the presence of singular behavior, substantially reducing the number of degrees of freedom required for the same accuracy with isotropic hp-refinement. This serves to bolster the relevance of RBS and full hp-adaptivity to a wide array of academic and industrial applications in CEM},
publisher={TechRxiv},
author={Corrado, Jeremiah and Harmon, Jake and Notaros, Branislav},
year={2021},
month={Oct}
}
@article{harmon:2021,
title={A Refinement-by-Superposition hp-Method for {H}(curl)- and {H}(div)-Conforming Discretizations},
url={https://www.techrxiv.org/articles/preprint/A_Refinement-by-Superposition_hp-Method_for_H_curl_-_and_H_div_-Conforming_Discretizations/14807895/1},
DOI={10.36227/techrxiv.14807895.v1},
abstractNote={We present an application of refinement-by-superposition (RBS) hp-refinement in computational electromagnetics (CEM), which permits exponential rates of convergence. In contrast to dominant approaches to hp-refinement for continuous Galerkin methods, which rely on constrained-nodes, the multi-level strategy presented drastically reduces the implementation complexity. Through the RBS methodology, enforcement of continuity occurs by construction, enabling arbitrary levels of refinement with ease and without the practical (but not theoretical) limitations of constrained-node refinement. We outline the construction of the RBS hp-method for refinement with H(curl)- and H(div)-conforming finite cells. Numerical simulations for the 2-D finite element method (FEM) solution of the Maxwell eigenvalue problem demonstrate the effectiveness of RBS hp-refinement. An additional goal of this work, we aim to promote the use of mixed-order (low- and high-order) elements in practical CEM applications.},
publisher={TechRxiv},
author={Harmon, Jake and Corrado, Jeremiah and Notaros, Branislav},
year={2021},
month={Jun}
}
@misc{nalgebra,
title = {Nalgebra: Linear algebra library for the {Rust} programming language},
year = {2021},
publisher = {GitHub},
journal = {GitHub repository},
url = {https://github.com/dimforge/nalgebra}
}
@article{slepc,
author = "Vicente Hernandez and Jose E. Roman and Vicente Vidal",
title = "{SLEPc}: A scalable and flexible toolkit for the solution of eigenvalue problems",
journal = "ACM Trans. Math. Software",
volume = "31",
number = "3",
pages = "351--362",
year = "2005",
DOI = {10.1145/1089014.1089019}
}
@misc{petsc-web-page,
author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed Brown
and Peter Brune and Kris Buschelman and Emil~M. Constantinescu and Lisandro Dalcin and Alp Dener
and Victor Eijkhout and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet
and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger
and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson
and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith
and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang},
title = {{PETS}c {W}eb page},
url = {https://petsc.org/},
year = {2021},
}
@techreport{petsc-user-ref,
author = {Satish Balay and Shrirang Abhyankar and Mark~F. Adams and Steven Benson and Jed Brown
and Peter Brune and Kris Buschelman and Emil Constantinescu and Lisandro Dalcin and Alp Dener
and Victor Eijkhout and William~D. Gropp and V\'{a}clav Hapla and Tobin Isaac and Pierre Jolivet
and Dmitry Karpeev and Dinesh Kaushik and Matthew~G. Knepley and Fande Kong and Scott Kruger
and Dave~A. May and Lois Curfman McInnes and Richard Tran Mills and Lawrence Mitchell and Todd Munson
and Jose~E. Roman and Karl Rupp and Patrick Sanan and Jason Sarich and Barry~F. Smith
and Stefano Zampini and Hong Zhang and Hong Zhang and Junchao Zhang},
title = {{PETSc/TAO} Users Manual},
institution = {Argonne National Laboratory},
number = {ANL-21/39 - Revision 3.16},
year = {2021},
}
@inproceedings{petsc-efficient,
author = {Satish Balay and William~D. Gropp and Lois Curfman McInnes and Barry~F. Smith},
title = {Efficient Management of Parallelism in Object Oriented Numerical Software Libraries},
booktitle = {Modern Software Tools in Scientific Computing},
editor = {E. Arge and A.~M. Bruaset and H.~P. Langtangen},
publisher = {Birkh{\"{a}}user Press},
pages = {163--202},
year = {1997},
DOI = {10.1007/978-1-4612-1986-6_8}
}
@article{dealII93,
title = {The \texttt{deal.II} Library, Version 9.3},
author = {Daniel Arndt and Wolfgang Bangerth and Bruno Blais and
Marc Fehling and Rene Gassm{\"o}ller and Timo Heister
and Luca Heltai and Uwe K{\"o}cher and Martin
Kronbichler and Matthias Maier and Peter Munch and
Jean-Paul Pelteret and Sebastian Proell and Konrad
Simon and Bruno Turcksin and David Wells and Jiaqi
Zhang},
journal = {Journal of Numerical Mathematics},
year = {2021},
url = {https://dealii.org/deal93-preprint.pdf},
doi = {10.1515/jnma-2021-0081},
volume = {29},
number = {3},
pages = {171--186}
}
@article{mfem,
title = {{MFEM}: A Modular Finite Element Methods Library},
author = {R. Anderson and J. Andrej and A. Barker and J. Bramwell and J.-S. Camier and
J. Cerveny V. Dobrev and Y. Dudouit and A. Fisher and Tz. Kolev and W. Pazner and
M. Stowell and V. Tomov and I. Akkerman and J. Dahm and D. Medina and S. Zampini},
journal = {Computers \& Mathematics with Applications},
doi = {10.1016/j.camwa.2020.06.009},
volume = {81},
pages = {42-74},
year = {2021}
}