Commit c27b29d9 authored by conmccoid's avatar conmccoid
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@article {mccoid_mini_17_davidenko1953new,
AUTHOR = {Davidenko, D. F.},
TITLE = {On a new method of numerical solution of systems of nonlinear
equations},
JOURNAL = {Doklady Akad. Nauk SSSR (N.S.)},
VOLUME = {88},
YEAR = {1953},
PAGES = {601--602},
MRCLASS = {65.0X},
MRNUMBER = {0054339},
MRREVIEWER = {A. S. Householder},
}
@article {mccoid_mini_17_branin1972widely,
AUTHOR = {Branin, Jr., F. H.},
TITLE = {Widely convergent method for finding multiple solutions of
simultaneous nonlinear equations},
JOURNAL = {IBM J. Res. Develop.},
FJOURNAL = {International Business Machines Corporation. Journal of
Research and Development},
VOLUME = {16},
YEAR = {1972},
PAGES = {504--522},
ISSN = {0018-8646},
MRCLASS = {65H10},
MRNUMBER = {418449},
DOI = {10.1147/rd.165.0504},
URL = {https://doi.org/10.1147/rd.165.0504},
}
@article {mccoid_mini_17_brent1972davidenko,
AUTHOR = {Brent, R. P.},
TITLE = {On the {D}avidenko-{B}ranin method for solving simultaneous
nonlinear equations},
NOTE = {Mathematics of numerical computation},
JOURNAL = {IBM J. Res. Develop.},
FJOURNAL = {International Business Machines Corporation. Journal of
Research and Development},
VOLUME = {16},
YEAR = {1972},
PAGES = {434--436},
ISSN = {0018-8646},
MRCLASS = {65H10},
MRNUMBER = {334498},
MRREVIEWER = {N. N. Abdelmalek},
DOI = {10.1147/rd.164.0434},
URL = {https://doi.org/10.1147/rd.164.0434},
}
@article {mccoid_mini_17_lui1999schwarz,
AUTHOR = {Lui, S. H.},
TITLE = {On {S}chwarz alternating methods for nonlinear elliptic
{PDE}s},
JOURNAL = {SIAM J. Sci. Comput.},
FJOURNAL = {SIAM Journal on Scientific Computing},
VOLUME = {21},
YEAR = {1999/00},
NUMBER = {4},
PAGES = {1506--1523},
ISSN = {1064-8275},
MRCLASS = {65N55 (65J15)},
MRNUMBER = {1756041},
MRREVIEWER = {Stephen W. Brady},
DOI = {10.1137/S1064827597327553},
URL = {https://doi.org/10.1137/S1064827597327553},
}
@article {mccoid_mini_17_Cai2002,
AUTHOR = {Cai, X-C. and Keyes, D. E.},
TITLE = {Nonlinearly preconditioned inexact {N}ewton algorithms},
JOURNAL = {SIAM J. Sci. Comput.},
FJOURNAL = {SIAM Journal on Scientific Computing},
VOLUME = {24},
YEAR = {2002},
NUMBER = {1},
PAGES = {183--200},
ISSN = {1064-8275},
MRCLASS = {65H10 (76M25)},
MRNUMBER = {1924420},
MRREVIEWER = {R. P. Tewarson},
DOI = {10.1137/S106482750037620X},
URL = {https://doi.org/10.1137/S106482750037620X},
}
@article {mccoid_mini_17_Dolean2016,
AUTHOR = {Dolean, V. and Gander, M. J. and Kheriji, W. and Kwok, F. and
Masson, R.},
TITLE = {Nonlinear preconditioning: how to use a nonlinear {S}chwarz
method to precondition {N}ewton's method},
JOURNAL = {SIAM J. Sci. Comput.},
FJOURNAL = {SIAM Journal on Scientific Computing},
VOLUME = {38},
YEAR = {2016},
NUMBER = {6},
PAGES = {A3357--A3380},
ISSN = {1064-8275},
MRCLASS = {65F08 (65F10 65N22 65N55)},
MRNUMBER = {3566907},
MRREVIEWER = {Judith M. Ford},
DOI = {10.1137/15M102887X},
URL = {https://doi.org/10.1137/15M102887X},
}
@incollection {mccoid_mini_17_Gander2017,
AUTHOR = {Gander, M. J.},
TITLE = {On the origins of linear and non-linear preconditioning},
BOOKTITLE = {Domain decomposition methods in science and engineering
{XXIII}},
SERIES = {Lect. Notes Comput. Sci. Eng.},
VOLUME = {116},
PAGES = {153--161},
PUBLISHER = {Springer, Cham},
YEAR = {2017},
MRCLASS = {65F08 (01A55 65-03)},
MRNUMBER = {3718350},
DOI = {10.1007/978-3-319-52389-7\_1},
URL = {https://doi.org/10.1007/978-3-319-52389-7_1},
}
@article {mccoid_mini_17_liu2015field,
AUTHOR = {Liu, L. and Keyes, D. E.},
TITLE = {Field-split preconditioned inexact {N}ewton algorithms},
JOURNAL = {SIAM J. Sci. Comput.},
FJOURNAL = {SIAM Journal on Scientific Computing},
VOLUME = {37},
YEAR = {2015},
NUMBER = {3},
PAGES = {A1388--A1409},
ISSN = {1064-8275},
MRCLASS = {65H10 (65H20 65N22 65N55)},
MRNUMBER = {3352613},
MRREVIEWER = {Luca Gemignani},
DOI = {10.1137/140970379},
URL = {https://doi.org/10.1137/140970379},
}
@book {mccoid_mini_17_gander2014scientific,
AUTHOR = {Gander, W. and Gander, M. J. and Kwok, F.},
TITLE = {Scientific computing},
SERIES = {Texts in Computational Science and Engineering},
VOLUME = {11},
NOTE = {An introduction using Maple and MATLAB},
PUBLISHER = {Springer, Cham},
YEAR = {2014},
PAGES = {xviii+905},
ISBN = {978-3-319-04324-1; 978-3-319-04325-8},
MRCLASS = {65-01},
MRNUMBER = {3287477},
DOI = {10.1007/978-3-319-04325-8},
URL = {https://doi.org/10.1007/978-3-319-04325-8},
}
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......@@ -523,7 +523,7 @@ For Schwarz methods, this would necessitate a theorem similar to Theorem \ref{th
% section on 2D extensions?
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%%%% This is a source file for an abstract of a contributed talk
%%%% at CH numerics day 2018
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%\usepackage{natbib} % Change this if you like but make sure what you do comes out ok
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\begin{document}
%Titel:
\begin{center}
{\bf Robust algorithms for the intersection of simplices}
\end{center}
\begin{center}
{\it Author and Presenter:} \\[0.5ex]
Conor McCoid (Universit\'e de Gen\`eve)
\end{center}
%Co-authors:
\begin{center}
{\it Co-authors:}\\[0.5ex]
\begin{tabular}{ll}
& Martin J. Gander (Universit\'e de Gen\`eve)\\
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\bigskip\noindent
%Abstract: max. 1 page
{\bf Abstract:} At times even the smallest of floating-point errors can cause intersection algorithms to destabilize.
The final result may then have an error several magnitudes larger.
Robust algorithms are then required to avoid such instabilities.
One way to achieve this is to write them parsimoniously \cite{fortune1989}, that is, by using the smallest number of direct calculations as necessary.
A given calculation may provide underutilized information that can eliminate the need for additional calculations.
In this talk we present methodology for maximizing information output of intersection calculations for $n$-simplices, with a focus on triangles \cite{mccoid2021} and tetrahedra.
\bigskip\noindent
\bibliographystyle{plain}
\begin{thebibliography}{1}
\bibitem{fortune1989} S.~Fortune,
Stable maintenance of point set triangulations in two dimensions.
Annual Symposium on Foundations of Computer Sicence (proceedings).
\bibitem{mccoid2021} C.~McCoid, M.~J.~Gander,
A provably robust algorithm for triangle-triangle intersections in floating-point arithmetic.
Transactions on Mathematical Software (in review).
\end{thebibliography}
\end{document}
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