ref.bib

@online{singh2021linear,
  title={On a linear stability issue of split form schemes for compressible flows},
  author={Singh, Vikram and Chandrashekar, Praveen},
  year={2021},
  eprint={2104.14941},
  eprinttype={arxiv},
  eprintclass={math.NA}
}

@misc{ranocha2021adaptiveRepro,
  title={Reproducibility repository for
         Adaptive numerical simulations with {T}rixi.jl:
         {A} case study of {J}ulia for scientific computing},
  author={Ranocha, Hendrik and Schlottke-Lakemper, Michael and Winters, Andrew Ross
          and Faulhaber, Erik and Chan, Jesse and Gassner, Gregor},
  year={2021},
  howpublished={\url{https://github.com/trixi-framework/paper-2021-juliacon}},
  doi={10.5281/zenodo.5201484}
}

@article{schlottkelakemper2021purely,
  title={A purely hyperbolic discontinuous {G}alerkin approach for
         self-gravitating gas dynamics},
  author={Schlottke-Lakemper, Michael and Winters, Andrew R and
          Ranocha, Hendrik and Gassner, Gregor J},
  journal={Journal of Computational Physics},
  pages={110467},
  year={2021},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2021.110467},
  eprint={2008.10593},
  eprinttype={arxiv},
  eprintclass={math.NA}
}

@article{ranocha2021preventing,
  title={Preventing pressure oscillations does not fix local linear stability
         issues of entropy-based split-form high-order schemes},
  author={Ranocha, Hendrik and Gassner, Gregor J},
  journal={Communications on Applied Mathematics and Computation},
  year={2021},
  doi={10.1007/s42967-021-00148-z},
  eprint={2009.13139},
  eprinttype={arxiv},
  eprintclass={math.NA}
}

@article{bezanson2017julia,
  title={Julia: {A} Fresh Approach to Numerical Computing},
  author={Bezanson, Jeff and Edelman, Alan and Karpinski, Stefan and
          Shah, Viral B},
  journal={SIAM Review},
  volume={59},
  number={1},
  pages={65--98},
  year={2017},
  publisher={SIAM},
  doi={10.1137/141000671},
  eprint={1411.1607},
  eprinttype={arxiv},
  eprintclass={cs.MS}
}

@article{rackauckas2017differentialequations,
  title={{DifferentialEquations.jl} {--} {A} Performant and Feature-Rich
         Ecosystem for Solving Differential Equations in {J}ulia},
  author={Rackauckas, Christopher and Nie, Qing},
  journal={Journal of Open Research Software},
  volume={5},
  number={1},
  pages={15},
  year={2017},
  publisher={Ubiquity Press},
  doi={10.5334/jors.151}
}

@online{revels2016forward,
  title={Forward-Mode Automatic Differentiation in {J}ulia},
  author={{Revels}, J. and {Lubin}, M. and {Papamarkou}, T.},
  year={2016},
  eprint={1607.07892},
  eprinttype={arxiv},
  eprintclass={cs.MS}
}

@inproceedings{byrne2021mpi,
  title={{MPI}.jl: {J}ulia bindings for the {M}essage {P}assing {I}nterface},
  author={Byrne, Simon and Wilcox, Lucas C and Churavy, Valentin},
  booktitle={Proceedings of the JuliaCon Conferences},
  volume={1},
  number={1},
  pages={68},
  year={2021},
  doi={10.21105/jcon.00068},
  note={\url{https://github.com/JuliaParallel/MPI.jl}}
}

@article{ranocha2021sbp,
  title={{SummationByPartsOperators.jl}: {A} {J}ulia library of provably stable
         semidiscretization techniques with mimetic properties},
  author={Ranocha, Hendrik},
  journal={Journal of Open Source Software},
  year={2021},
  month={08},
  doi={10.21105/joss.03454},
  volume={6},
  number={64},
  pages={3454},
  publisher={The Open Journal},
  url={https://github.com/ranocha/SummationByPartsOperators.jl}
}

@online{innes2018fashionable,
  title={Fashionable Modelling with {F}lux},
  author={Innes, Michael and Saba, Elliot and Fischer, Keno and Gandhi, Dhairya
          and Rudilosso, Marco Concetto and Joy, Neethu Mariya and Karmali, Tejan
          and Pal, Avik and Shah, Viral},
  year={2018},
  eprint={1811.01457},
  eprinttype={arxiv},
  eprintclass={cs.PL}
}

@article{dunning2017jump,
  title={{JuMP}: A modeling language for mathematical optimization},
  author={Dunning, Iain and Huchette, Joey and Lubin, Miles},
  journal={SIAM Review},
  volume={59},
  number={2},
  pages={295--320},
  year={2017},
  publisher={SIAM},
  doi={10.1137/15M1020575}
}

@inproceedings{olver2014practical,
  title={A practical framework for infinite-dimensional linear algebra},
  author={Olver, Sheehan and Townsend, Alex},
  booktitle={2014 First Workshop for High Performance Technical Computing
             in Dynamic Languages},
  pages={57--62},
  year={2014},
  organization={IEEE},
  doi={10.1109/HPTCDL.2014.10},
  note={Software available at \url{https://github.com/JuliaApproximation/ApproxFun.jl}}
}

@article{constantinou2021geophysicalflows,
  title={{GeophysicalFlows}.jl: {S}olvers for geophysical fluid dynamics problems
         in periodic domains on {CPUs} \& {GPUs}},
  author={Constantinou, Navid C and Wagner, Gregory LeClaire and Siegelman, Lia
          and Pearson, Brodie C and Pal{\'o}czy, Andr{\'e}},
  journal={Journal of Open Source Software},
  volume={6},
  number={60},
  pages={3053},
  year={2021},
  doi={10.21105/joss.03053}
}

@article{badia2020gridap,
  title={Gridap: {A}n extensible Finite Element toolbox in {J}ulia},
  author={Badia, Santiago and Verdugo, Francesc},
  journal={Journal of Open Source Software},
  volume={5},
  number={52},
  pages={2520},
  year={2020},
  doi={10.21105/joss.02520}
}

@article{ramadhan2020oceananigans,
  title={Oceananigans.jl: {F}ast and friendly geophysical fluid dynamics
         on {GPU}s},
  author={Ramadhan, Ali and Wagner, Gregory LeClaire and Hill, Chris and
          Campin, Jean-Michel and Churavy, Valentin and Besard, Tim and
          Souza, Andre and Edelman, Alan and Ferrari, Raffaele and
          Marshall, John},
  journal={Journal of Open Source Software},
  volume={5},
  number={53},
  pages={2018},
  year={2020},
  doi={10.21105/joss.02018}
}

@online{pal2021opening,
  title={Opening the Blackbox: Accelerating Neural Differential Equations by
         Regularizing Internal Solver Heuristics},
  author={Pal, Avik and Ma, Yingbo and Shah, Viral and Rackauckas, Christopher},
  year={2021},
  eprint={2105.03918},
  eprinttype={arxiv},
  eprintclass={cs.LG}
}

@article{krais2021flexi,
  title={{FLEXI}: {A} high order discontinuous {G}alerkin framework for
         hyperbolic-parabolic conservation laws},
  author={Krais, Nico and Beck, Andrea and Bolemann, Thomas and Frank, Hannes
          and Flad, David and Gassner, Gregor and Hindenlang, Florian and
          Hoffmann, Malte and Kuhn, Thomas and Sonntag, Matthias and
          Munz, Claus-Dieter},
  journal={Computers \& Mathematics with Applications},
  volume={81},
  pages={186--219},
  year={2021},
  publisher={Elsevier},
  doi={10.1016/j.camwa.2020.05.004}
}

@article{parsani2021ssdc,
  title={High-order accurate entropy-stable discontinuous collocated {G}alerkin
         methods with the summation-by-parts property for compressible
         {CFD} frameworks: {S}calable {SSDC} algorithms and flow solver},
  author={Parsani, Matteo and Boukharfane, Radouan and Nolasco, Irving Reyna and
          Fern{\'a}ndez, David C Del Rey and Zampini, Stefano and Hadri, Bilel
          and Dalcin, Lisandro},
  journal={Journal of Computational Physics},
  volume={424},
  pages={109844},
  year={2021},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2020.109844}
}

@article{burstedde2011p4est,
  title={\texttt{p4est}: {S}calable algorithms for parallel adaptive mesh
         refinement on forests of octrees},
  author={Burstedde, Carsten and Wilcox, Lucas C and Ghattas, Omar},
  journal={SIAM Journal on Scientific Computing},
  volume={33},
  number={3},
  pages={1103--1133},
  year={2011},
  publisher={SIAM},
  doi={10.1137/100791634},
  note={\url{https://github.com/cburstedde/p4est}}
}

@article{barnes2010publish,
  title={Publish your computer code: it is good enough},
  author={Barnes, Nick},
  journal={Nature},
  volume={467},
  number={7317},
  year={2010},
  doi={10.1038/467753a}
}

@article{donoho2010invitation,
  title={An invitation to reproducible computational research},
  author={Donoho, David L},
  journal={Biostatistics},
  volume={11},
  number={3},
  pages={385--388},
  year={2010},
  publisher={Oxford University Press},
  doi={10.1093/biostatistics/kxq028}
}

@article{leveque2013top,
  title={Top ten reasons to not share your code (and why you should anyway)},
  author={LeVeque, Randall J},
  journal={SIAM News},
  volume={46},
  number={3},
  year={2013}
}

@article{ranocha2021optimized,
  title={Optimized {R}unge-{K}utta Methods with Automatic Step Size Control
         for Compressible Computational Fluid Dynamics},
  author={Ranocha, Hendrik and Dalcin, Lisandro and Parsani, Matteo
          and Ketcheson, David I.},
  journal={Communications on Applied Mathematics and Computation},
  year={2021},
  month={11},
  doi={10.1007/s42967-021-00159-w},
  eprint={2104.06836},
  eprinttype={arxiv},
  eprintclass={math.NA}
}

@article{besard2018juliagpu,
  title={Effective Extensible Programming: Unleashing {Julia} on {GPUs}},
  author={Besard, Tim and Foket, Christophe and De Sutter, Bjorn},
  journal={IEEE Transactions on Parallel and Distributed Systems},
  year={2018},
  doi={10.1109/TPDS.2018.2872064},
  eprint={1712.03112},
  eprinttype={arxiv},
  eprintclass={cs.PL}
}

@online{omlin2020solving,
  title={Solving Nonlinear Multi-Physics on {GPU} Supercomputers with {J}ulia},
  author={Omlin, Samuel and Räss, Ludovic and Kwasniewski, Grzegorz and
          Malvoisin, Benjamin and Podladchikov, Yury},
  howpublished={\url{https://www.youtube.com/watch?v=vPsfZUqI4_0}. Talk presented at JuliaCon},
  location={virtual},
  year={2020},
}

@article{grassi2014krome,
  title={{KROME} -- a package to embed chemistry in astrophysical simulations},
  author={Grassi, T and Bovino, S and Schleicher, DRG and Prieto, J and Seifried, D
          and Simoncini, E and Gianturco, FA},
  journal={Monthly Notices of the Royal Astronomical Society},
  volume={439},
  number={3},
  pages={2386--2419},
  year={2014},
  publisher={Oxford University Press},
  doi={10.1093/mnras/stu114}
}

@book{hesthaven2007nodal,
  title={Nodal Discontinuous {G}alerkin Methods: {A}lgorithms, Analysis, and
         Applications},
  author={Hesthaven, Jan S and Warburton, Tim},
  series={Texts in Applied Mathematics},
  volume={54},
  year={2007},
  publisher={Springer Science \& Business Media},
  address={New York},
  doi={10.1007/978-0-387-72067-8}
}

@book{kopriva2009implementing,
  title={Implementing Spectral Methods for Partial Differential Equations:
         {A}lgorithms for Scientists and Engineers},
  author={Kopriva, David A},
  year={2009},
  publisher={Springer Science \& Business Media},
  address={New York},
  doi={10.1007/978-90-481-2261-5}
}

@article{tadmor1987numerical,
  title={The numerical viscosity of entropy stable schemes for systems of
         conservation laws. {I}},
  author={Tadmor, Eitan},
  journal={Mathematics of Computation},
  volume={49},
  number={179},
  pages={91--103},
  year={1987},
  publisher={American Mathematical Society},
  doi={10.1090/S0025-5718-1987-0890255-3}
}

@article{lefloch2002fully,
  title={Fully Discrete, Entropy Conservative Schemes of Arbitrary Order},
  author={LeFloch, Philippe G and Mercier, Jean-Marc and Rohde, Christian},
  journal={SIAM Journal on Numerical Analysis},
  volume={40},
  number={5},
  pages={1968--1992},
  year={2002},
  publisher={Society for Industrial and Applied Mathematics},
  doi={10.1137/S003614290240069X}
}

@article{fisher2013high,
  title={High-order entropy stable finite difference schemes for nonlinear
         conservation laws: {F}inite domains},
  author={Fisher, Travis C and Carpenter, Mark H},
  journal={Journal of Computational Physics},
  volume={252},
  pages={518--557},
  year={2013},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2013.06.014}
}

@article{ranocha2018comparison,
  title={Comparison of Some Entropy Conservative Numerical Fluxes for the {E}uler
         Equations},
  author={Ranocha, Hendrik},
  journal={Journal of Scientific Computing},
  volume={76},
  number={1},
  pages={216--242},
  year={2018},
  publisher={Springer},
  doi={10.1007/s10915-017-0618-1},
  eprint={1701.02264},
  eprinttype={arxiv},
  eprintclass={math.NA}
}

@article{chen2017entropy,
  title={Entropy stable high order discontinuous {G}alerkin methods with suitable
         quadrature rules for hyperbolic conservation laws},
  author={Chen, Tianheng and Shu, Chi-Wang},
  journal={Journal of Computational Physics},
  volume={345},
  pages={427--461},
  year={2017},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2017.05.025}
}

@article{ewert2003acoustic,
  title={Acoustic perturbation equations based on flow decomposition via source filtering},
  author={Ewert, Roland and Schr{\"o}der, Wolfgang},
  journal={Journal of Computational Physics},
  volume={188},
  number={2},
  pages={365--398},
  year={2003},
  publisher={Elsevier},
  doi={10.1016/S0021-9991(03)00168-2}
}

@article{chan2019efficient,
  title={Efficient entropy stable {G}auss collocation methods},
  author={Chan, Jesse and Del Rey Fern{\'a}ndez, David C and Carpenter, Mark H},
  journal={SIAM Journal on Scientific Computing},
  volume={41},
  number={5},
  pages={A2938--A2966},
  year={2019},
  publisher={SIAM},
  doi={10.1137/18M1209234},
  doi={10.1137/18M1209234}
}

@techreport{CarpenterKennedy1994,
  title={Fourth Order {2N}-Storage {R}unge-{K}utta Schemes},
  author={Kennedy, Christopher A and Carpenter, Mark H},
  institution={NASA},
  year={1994},
  type={Technical Memorandum},
  number={NASA-TM-109112},
  address={NASA Langley Research Center, Hampton VA 23681-0001, United States}
}

@article{gassner2011,
	author={Gassner, Gregor J. and Hindenlang, Florian and Munz, Claus-Dieter},
	journal={Adaptive High-Order Methods in Computational Fluid Dynamics},
	pages={95--118},
	publisher={World Scientific Publishing Company Incorporated},
	title={A {R}unge-{K}utta Based discontinuous {G}alerkin method with time accurate local time stepping},
	volume={2},
	year={2011},
  doi={10.1142/9789814313193\_0004}
}

@phdthesis{altmann2012,
	author={Christoph Altmann},
	school={University of Stuttgart, Germany},
	title={Explicit discontinuous {G}alerkin methods for magnetohydrodynamics},
	year={2012},
  doi={10.18419/opus-3895}
}

@article{bohm2020,
  author={Marvin Bohm and Andrew R. Winters and Gregor J. Gassner and Dominik Derigs and Florian Hindenlang and Joachim Saur},
  title={An entropy stable nodal discontinuous {G}alerkin method for the resistive {MHD} equations. {P}art {I}: {T}heory and numerical verification},
  journal={Journal of Computational Physics},
  volume={422},
  pages={108076},
  year={2020},
  doi={10.1016/j.jcp.2018.06.027}
}

@book{Toro2009,
  title={Riemann Solvers and Numerical Methods for Fluid Dynamics: {A} Practical
         Introduction},
  author={Toro, Eleuterio F},
  year={2009},
  publisher={Springer},
  address={Berlin Heidelberg},
  doi={10.1007/b79761}
}

 @article{li2005hllc,
  title={An {HLLC} {R}iemann solver for magneto-hydrodynamics},
  author={Li, Shengtai},
  journal={Journal of Computational Physics},
  volume={203},
  number={1},
  pages={344--357},
  year={2005},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2004.08.020}
}

@inproceedings{ranocha2020icosahom,
  author={Ranocha, Hendrik},
  editor={Sherwin, Spencer J. and Moxey, David and Peir{\'o}, Joaquim and Vincent, Peter E. and Schwab, Christoph},
  title={Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the {E}uler Equations Using Summation-by-Parts Operators},
  booktitle={Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018},
  year={2020},
  publisher={Springer International Publishing},
  address={Cham},
  pages={525--535},
  isbn={978-3-030-39647-3},
  doi={10.1007/978-3-030-39647-3\_42}
}

@phdthesis{ranocha2018thesis,
  title={Generalised Summation-by-Parts Operators and Entropy Stability of
         Numerical Methods for Hyperbolic Balance Laws},
  author={Ranocha, Hendrik},
  year={2018},
  school={TU~Braunschweig, Germany},
  isbn={9783736997356}
}

@misc{hindenlang2019,
  title={A new entropy conservative two-point flux for ideal {MHD} equations derived from first principles},
  author={Florian Hindenlang and Gregor J. Gassner},
  howpublished={Talk presented at HONOM 2019: European workshop on high order numerical methods},
  location={Madrid, Spain},
  year={2019},
}

@article{gassner2016split,
  title={Split form nodal discontinuous {G}alerkin schemes with summation-by-parts property for the compressible {E}uler equations},
  author={Gassner, Gregor J and Winters, Andrew R and Kopriva, David A},
  journal={Journal of Computational Physics},
  volume={327},
  pages={39--66},
  year={2016},
  publisher={Elsevier},
  doi={10.1016/j.jcp.2016.09.013}
}

@phdthesis{gassner2009,
	author={Gregor Gassner},
	school={University of Stuttgart, Germany},
	title={Discontinuous {G}alerkin methods for the unsteady compressible {N}avier-{S}tokes equations},
	year={2009},
  doi={10.18419/opus-3788}
}

@misc{hendrik_blog,
  author = {Hendrik Ranocha},
  title = {Optimizing {J}ulia code: {I}mproving the performance of entropy-conservative {DG} methods in {T}rixi.jl},
  year = {2021},
  howpublished={\url{https://ranocha.de/blog/Optimizing_EC_Trixi}}
}

@online{ranocha2021efficient,
  title={Efficient implementation of modern entropy stable and kinetic energy
         preserving discontinuous {G}alerkin methods for conservation laws},
  author={Ranocha, Hendrik and Schlottke-Lakemper, Michael and Chan, Jesse and
          Rueda-Ram\'{i}rez, Andr{\'e}s M and Winters, Andrew R and
          Hindenlang, Florian and Gassner, Gregor J},
  year={2021},
  month={12},
  eprint={2112.10517},
  eprinttype={arxiv},
  eprintclass={cs.MS}
}

@online{liu2021oscillation,
  title={An Oscillation-free Discontinuous {G}alerkin Method for Hyperbolic
         Systems},
  author={Liu, Yong and Lu, Jianfang and Shu, Chi-Wang},
  year={2021},
  howpublished={\url{https://www.brown.edu/research/projects/scientific-computing/sites/brown.edu.research.projects.scientific-computing/files/uploads/AN%20OSCILLATION-FREE%20DISCONTINUOUS%20GALERKIN%20METHOD%20FOR%20HYPERBOLIC%20SYSTEMS%20.pdf}}
}

@INPROCEEDINGS{hunold2020benchmarking,
  author={Hunold, Sascha and Steiner, Sebastian},
  booktitle={{2020 IEEE/ACM Performance Modeling, Benchmarking and Simulation of High Performance
             Computer Systems (PMBS)}},
  title={{Benchmarking Julia's Communication Performance: Is Julia HPC ready or Full HPC?}},
  year={2020},
  pages={20-25},
  doi={10.1109/PMBS51919.2020.00008}
}


@INPROCEEDINGS{frings2013parallelloading,
  author={Wolfgang Frings and Dong Ahn and Matthew LeGendre and Todd Gamblin and Bronis de Supinski
          and Felix Wolf},
  booktitle={{27th International Conference on Supercomputing, Eugene, OR, USA}},
  title={{Massively Parallel Loading}},
  year={2013},
  pages={389--398},
  doi={10.1145/2464996.2465020}
}

@inproceedings{gamblin2015spack,
author = {Gamblin, Todd and LeGendre, Matthew and Collette, Michael R. and Lee, Gregory L. and Moody, Adam and de Supinski, Bronis R. and Futral, Scott},
title = {{The Spack Package Manager: Bringing Order to HPC Software Chaos}},
year = {2015},
isbn = {9781450337236},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
doi = {10.1145/2807591.2807623},
booktitle = {Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis},
articleno = {40},
numpages = {12},
location = {Austin, Texas},
series = {SC '15}
}