vmec_refs.bib

@article{merkel_1982,
  title={{A Green’s Function Method for the Vacuum Contribution to the MHD Stability of Helically Symmetric Equilibria}},
  author={Merkel, P.},
  year={1982},
  journal={Z. Naturforsch.},
  volume={37a},
  number={8},
  pages={859--865},
  doi={10.1515/zna-1982-0819},
}


@article{hirshman_whitson_1983,
title={Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria},
author={S. P. Hirshman and J. C. Whitson},
year={1983},
journal={Phys. Fluids},
volume={26},
pages={3553--3568},
doi={10.1063/1.864116}
}

@article{hirshman_meier_1985,
  author = {Hirshman, S. P. and Meier, H. K.},
  title = {{Optimized Fourier representations for three‐dimensional magnetic surfaces}},
  year = {1985},
  journal = {Phys. Fluids},
  volume = {28},
  number = {5},
  pages = {1387--1391},
  doi = {10.1063/1.864972},
}

@article{hirshman_lee_1986,
  author = {S. P. Hirshman and D. K. Lee},
  title = {{MOMCON: A spectral code for obtaining three-dimensional magnetohydrodynamic equilibria}},
  year = {1986},
  journal = {Comp. Phys. Comm.},
  volume = {39},
  number = {2},
  pages = {161--172},
  doi = {10.1016/0010-4655(86)90127-X},
}

@article{hirshman_hogan_1986,
  title={{ORMEC: A three-dimensional MHD spectral inverse equilibrium code}},
  author={Hirshman, S. P. and Hogan, J. T.},
  year={1986},
  journal={J. Comp. Phys.},
  volume={63},
  number={2},
  pages={329--352},
  doi={10.1016/0021-9991(86)90197-X},
}


@article{merkel_1986,
  title={{An Integral Equation Technique for the Exterior and Interior Neumann Problem in Toroidal Regions}},
  author={Merkel, P.},
  year={1986},
  journal={J. Comp. Phys.},
  volume={66},
  number={1},
  pages={83--98},
  doi={10.1016/0021-9991(86)90055-0},
}


@article{hirshman_vanrij_merkel_1986,
  title={{Three-dimensional free boundary calculations using a spectral Green's function method}},
  author={Hirshman, S. P. and van Rij, W. I. and Merkel, P.},
  year={1986},
  journal={Comp. Phys. Comm.},
  volume={43},
  number={1},
  pages={143--155},
  doi={10.1016/0010-4655(86)90058-5},
}



@article{attenberger_1987,
  title={{Some Practial Considerations Involving Spectral Representations of 3D Plasma Equilibria}},
  author={S. E. Attenberger and W. A. Houlberg and S. P. Hirshman},
  year={1987},
  journal={J. Comput. Phys.},
  volume={72},
  pages={435--448},
  doi={10.1016/0021-9991(87)90092-1},
}

@article{hirshman_schwenn_nuehrenberg_1990,
  title={{Improved Radial Differencing for Three-Dimensional Magnetohydrodynamic Equilibrium Calculations}},
  author={Hirshman, S. P. and Schwenn, U. and N{\"u}hrenberg, J.},
  year={1990},
  journal={J. Comp. Phys.},
  volume={87},
  number={2},
  pages={396--407},
  doi={10.1016/0021-9991(90)90259-4},
}

@article{hirshman_betancourt_1991,
  title={{Preconditioned Descent Algorithm for Rapid Calculations of Magnetohydrodynamic Equilibria}},
  author={Hirshman, S. P. and Betancourt, O.},
  year={1991},
  journal={J. Comp. Phys.},
  volume={96},
  number={1},
  pages={99--109},
  doi={10.1016/0021-9991(91)90267-O},
}

@article{hirshman_breslau_1998,
  title={{Explicit spectrally optimized Fourier series for nested magnetic surfaces}},
  author={Hirshman, S. P. and Breslau, J.},
  year={1998},
  journal={Phys. Plasmas},
  volume={5},
  number={7},
  pages={2664--2675},
  doi={10.1063/1.872954},
}

@article{hirshman_etal_2010,
  title={{BCYCLIC: A parallel block tridiagonal matrix cyclic solver}},
  author={Hirshman, S. P. and Perumalla, K. S. and Lynch, V. E. and Sanchez, R.},
  year={2010},
  journal={J. Comp. Phys.},
  volume={229},
  number={18},
  pages={6392--6404},
  doi={10.1016/j.jcp.2010.04.049},
}

@inproceedings{seal_hirshman_2016,
  title={{PARVMEC: An Efficient, Scalable Implementation of the Variational Moments Equilibrium Code}},
  author={Seal, S. K. and Hirshman, S. P. and Wingen, A. and Wilcox, R. S. and Cianciosa, M. R. and Unterberg, E. A.},
  year={2016},
  booktitle={{2016 45th International Conference on Parallel Processing (ICPP)}},
  pages={618--627},
  organization={IEEE},
  doi={10.1109/ICPP.2016.77},
}

@inproceedings{merkel_1987,
  title={{Application of the Neumann problem on stellarators: Magnetic surface, coils, free boundary equilibrium, magnetic diagnostics}},
  author={Merkel, P.},
  year={1987},
  booktitle={{International School of Plasma Physics}},
  pages={25--46},
  doi={},
}
Proc. Theory of Fusion Plasmas,  Piero Caldirola, Varenna, Italy, 24–28 August 1987, EUR 11336EN (1987), p. 25

@book{roy_2007,
  title={{Potential Theory in Applied Geophysics}},
  author={Roy, Kalyan Kumar},
  year={2007},
  publisher={Springer Science \& Business Media}
}

@book{gradshteyn_ryzhik,
  title={{Table of Integrals, Series and Products (Eigth Edition)}},
  author={{Gradshteyn, I. S. and Ryzhik, I. M.}},
  year={2015},
  publisher={Academic Press (Elsevier)},
}











@article{strumberger_2002,
  author = {E. Strumberger and S. Günter and P. Merkel and E. Schwarz and C. Tichmann and H.-P. Zehrfeld},
  title = {Numerical computation of magnetic fields of two- and three-dimensional equilibria with net toroidal current},
  year = 2002,
  journal = {Nucl. Fusion},
  volume = {42},
  number = {7},
  pages = {827--832},
  doi = {10.1088/0029-5515/42/7/305},
}

@article{hanson_2009,
title={{V3FIT: a code for three-dimensional equilibrium reconstruction}},
author={James D. Hanson and Steven P. Hirshman and Stephen F. Knowlton and Lang L. Lao and Edward A. Lazarus and John M. Shields},
journal={Nucl. Fusion},
volume={49},
pages={075031},
year={2009},
doi = {10.1088/0029-5515/49/7/075031},
}






@article{howell_hanson_2020,
  title={{Development of a non-parametric Gaussian process model in the three-dimensional equilibrium reconstruction code V3FIT}},
  volume={86},
  DOI={10.1017/S0022377819000813},
  number={1},
  journal={J. Plasma Phys.},
  publisher={Cambridge University Press},
  author={Howell, Eric C. and Hanson, J. D.},
  year={2020},
  pages={905860102}
}

@book{discrete_mathematics,
  title     = {{Discrete Mathematics: An Open Introduction}},
  author    = {Levin, Oscar},
  year      = 2018,
  publisher = {University of Northern Colorado},
  address   = {Colorado},
  url = {http://discrete.openmathbooks.org/dmoi2/section-27.html#subsection-41}
}

@inproceedings{merkel_1988,
  title={{Applications of the Neumann Problem to Stellarators: Magnetic Surfaces, Coils, Free-Boundary Equilibrium, Magnetic Diagnostics}},
  author={Merkel, P.},
  editor={Bondeson, A. and Sindoni, E. and Troyon, F.},
  year={1988},
  booktitle={{Theory of Fusion Plasmas}},
  pages={25--46},
  url={http://hdl.handle.net/11858/00-001M-0000-0028-BDF5-4},
}

@inproceedings{romero_1998,
  author={Romero, Luis F. and Ortigosa, Eva M. and Zapata, Emilio L. and Jim{\'e}nez, Juan A.},
  title={{Parallelization Strategies for the VMEC Program}},
  year={1998},
  pages={483--490},
  editor={K{\aa}gstr{\"o}m, Bo and Dongarra, Jack and Elmroth, Erik and Wa{\'{s}}niewski, Jerzy},
  booktitle={Applied Parallel Computing Large Scale Scientific and Industrial Problems},
  publisher={Springer Berlin Heidelberg},
  address={Berlin, Heidelberg},
}

@thesis{msc_zhou,
  title={{Partial parallelization of VMEC system}},
  author={Mei Zhou},
  type={mathesis},
  year={1999},
  institution={Department of Computer Science, University of Montana},
  url={https://scholarworks.umt.edu/etd/5507}
}

@article{romero_2001,
  title = {{Data-task parallelism for the VMEC program}},
  author = {L.F. Romero and E.M. Ortigosa and E.L. Zapata},
  year = {2001},
  journal = {Parallel Computing},
  volume = {27},
  number = {10},
  pages = {1347-1364},
  issn = {0167-8191},
  doi = {https://doi.org/10.1016/S0167-8191(01)00094-1},
  keywords = {Data parallelism, Functional decomposition, Communication overlapping, Load balancing},
}

@article{merz_2013,
  title={{Optimization strategy for the VMEC stellarator equilibrium code}},
  author={Merz, F. and Geiger, J. and Rampp, M.},
  year={2013},
  journal={IPP R/48},
  url={http://hdl.handle.net/11858/00-001M-0000-0026-E182-5}
}

@article{strumberger_2005,
  title={{User Manual: Iterative Computation of 3D Ideal MHD Equilibria and Magnetic Fields}},
  author={Strumberger, E. and Hölzl, M.},
  year={2005},
  journal={IPP 5/113},
  url={http://hdl.handle.net/11858/00-001M-0000-0027-16AA-6}
}

@article{hudson_knotatrons,
  author = {Hudson,S. R.  and Startsev,E.  and Feibush,E. },
  title = {A new class of magnetic confinement device in the shape of a knot},
  journal = {Physics of Plasmas},
  volume = {21},
  number = {1},
  pages = {010705},
  year = {2014},
  doi = {10.1063/1.4863844},
}

@article{dewar_hudson_1998_stellarator_symmetry,
  title = {Stellarator symmetry},
  author = {R.L. Dewar and S.R. Hudson},
  journal = {{Physica D}},
  volume = {112},
  number = {1},
  pages = {275-280},
  year = {1998},
  doi = {10.1016/S0167-2789(97)00216-9},
}

@Article{FFTW05,
  author = 	 {Frigo, Matteo and Johnson, Steven~G.},
  title = 	 {{The Design and Implementation of {FFTW3}}},
  journal = 	 {Proceedings of the IEEE},
  year = 	 2005,
  volume =	 93,
  number =	 2,
  pages =	 {216--231},
  note =	 {Special issue on ``Program Generation, Optimization, and Platform Adaptation''}
}

@book{martensen_potentialtheorie,
  author={Erich Martensen},
  title={{Potentialtheorie}},
}


@article{y1972_shafranov_zakharov,
	doi = {10.1088/0029-5515/12/5/009},
	url = {https://doi.org/10.1088%2F0029-5515%2F12%2F5%2F009},
	year = 1972,
	month = {sep},
	publisher = {{IOP} Publishing},
	volume = {12},
	number = {5},
	pages = {599--601},
	author = {Shafranov, V. D. and Zakharov, L. E.},
	title = {Use of the virtual-casing principle in calculating the containing magnetic field in toroidal plasma systems},
	journal = {Nucl. Fusion},
}

@article{y1985_hirshman,
	author = {Hirshman, S. P. and Meier, H. K.},
	title = {{Optimized Fourier representations for three‐dimensional magnetic surfaces}},
	journal = {Phys. Fluids},
	volume = {28},
	number = {5},
	pages = {1387-1391},
	year = {1985},
	doi = {10.1063/1.864972},
	URL = {https://aip.scitation.org/doi/abs/10.1063/1.864972},
	eprint = {https://aip.scitation.org/doi/pdf/10.1063/1.864972}
}

@article{y1998_hirshman,
	author = {Hirshman, S. P. and Breslau, J.},
	title = {{Explicit spectrally optimized Fourier series for nested magnetic surfaces}},
	journal = {Phys. Plas.},
	volume = {5},
	number = {7},
	pages = {2664-2675},
	year = {1998},
	doi = {10.1063/1.872954},
	URL = {https://doi.org/10.1063/1.872954},
	eprint = {https://doi.org/10.1063/1.872954}
}

@article{y2010_hirshman,
	title = {{BCYCLIC: A parallel block tridiagonal matrix cyclic solver}},
	journal = {J. Comp. Phys.},
	volume = {229},
	number = {18},
	pages = {6392 - 6404},
	year = {2010},
	issn = {0021-9991},
	doi = {https://doi.org/10.1016/j.jcp.2010.04.049},
	url = {http://www.sciencedirect.com/science/article/pii/S0021999110002536},
	author = {Hirshman, S.P. and Perumalla, K. S. and Lynch, V. E. and Sanchez, R.},
}

@article{y2011_hudson,
	doi = {10.1088/0741-3335/54/1/014005},
	url = {https://doi.org/10.1088%2F0741-3335%2F54%2F1%2F014005},
	year = 2011,
	month = {dec},
	publisher = {{IOP} Publishing},
	volume = {54},
	number = {1},
	pages = {014005},
	author = {Hudson, S. R. and Dewar, R. L. and Hole, M. J. and McGann, M.},
	title = {Non-axisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions},
	journal = {Plasma Phys. and Contr. Fusion}
}

@article{y2012_lazerson,
	doi = {10.1088/0741-3335/54/12/122002},
	url = {https://doi.org/10.1088%2F0741-3335%2F54%2F12%2F122002},
	year = 2012,
	month = {nov},
	publisher = {{IOP} Publishing},
	volume = {54},
	number = {12},
	pages = {122002},
	author = {Lazerson, S. A.},
	title = {{The virtual-casing principle for 3D toroidal systems}},
	journal = {Plasma Phys. and Contr. Fusion}
}

@article{y2013_lazerson,
	doi = {10.1088/0741-3335/55/2/025014},
	url = {https://doi.org/10.1088%2F0741-3335%2F55%2F2%2F025014},
	year = 2013,
	month = {jan},
	publisher = {{IOP} Publishing},
	volume = {55},
	number = {2},
	pages = {025014},
	author = {Lazerson, S. A. and Sakakibara, S. and Suzuki, Y.},
	title = {{A magnetic diagnostic code for 3D fusion equilibria}},
	journal = {Plasma Phys. and Contr. Fusion}
}

@article{y2015_hanson,
	doi = {10.1088/0741-3335/57/11/115006},
	url = {https://doi.org/10.1088%2F0741-3335%2F57%2F11%2F115006},
	year = 2015,
	month = {sep},
	publisher = {{IOP} Publishing},
	volume = {57},
	number = {11},
	pages = {115006},
	author = {Hanson, J. D.},
	title = {{The virtual-casing principle and Helmholtz's theorem}},
	journal = {Plasma Phys. and Contr. Fusion}
}

@article{y2017_zhu,
	doi = {10.1088/1741-4326/aa8e0a},
	url = {https://doi.org/10.1088%2F1741-4326%2Faa8e0a},
	year = 2017,
	month = {nov},
	publisher = {{IOP} Publishing},
	volume = {58},
	number = {1},
	pages = {016008},
	author = {Zhu, C. and Hudson, S. R. and Song, Y. and Wan, Y.},
	title = {New method to design stellarator coils without the winding surface},
	journal = {Nucl. Fusion}
}