------------------------------------ MIMETIC DISCRETIZATIONS BIBLIOGRAPHY ------------------------------------ Stripped down BibTeX file Nicolas Robidoux and Stanly Steinberg March 22, 2003 --------------------IMPORTANT NOTE-------------------- YOU DO NOT NEED TO MODIFY THIS FILE TO GENERATE A LATEX BIBLIOGRAPHY WITH BIBTEX. BibTeX ignores---that is, treats as a comment---anything which does not start with the "at" character ("at" marks the beginnings of BibTeX entries; see below). This paragraph, for example, does not exist as far as BibTeX is concerned. Instructions on how to generate a bibliography from this file are found below. This is quite easy provided you have LaTeX installed. (LaTeX is free and available for "all" operating systems, including Windows, Mac and Unix.) ------------------------------------------------------ Please send corrections/updates/additions/comments to "Nicolas Robidoux" (See comments above about "at" in .bib files.) The most current version is found at http://www.math.sfu.ca/~nrobidou/public_html/mimetic/mimetic.bib http://www.math.sfu.ca/~nrobidou/public_html/mimetic/mimetic2.bib is a richly annotated version of the same file, which is not suitable for creating publication ready bibliographies. Visit http://www.math.sfu.ca/~nrobidou/public_html/mimetic/mimetic.html for additional documents. ---------------------------------------------------------------------- 1998Bossavit, 1991BossavitB, 2001HiptmairB and 1996Shashkov have excellent bibliographies which I hope to merge come "manana." You will also find additional relevant articles and books by searching the authors in the online version of Mathematical Reviews: http://www.ams.org/mathscinet (by subscription). Although the philosophy behind "geometric integration" methods for ODEs is fairly similar to that behind "mimetic discretizations," geometric integration articles are not included here unless they relate directly to mimetic methods for PDEs. A geometric integration bibliography is found at http://www.math.ntnu.no/num/synode/bib/geom_int/geom_int.html Also: Although articles about finite volume methods for the integration of hyperbolic conservation laws (e.g., CFD) probably should be included, this bibliography is quite sparse on this topic. On the other hand, the bibliography also contains related entries from the field of computer graphics. "Recommended" articles and books (see the NOTE fields) reflect my (Nicolas Robidoux) biases and weight readability and perspective more than historical importance and technical achievement. Note that many articles without a recommendation are so because I have not read them carefully enough to have a clear opinion. Send preprints/reprints to Nicolas Robidoux PIMS, EAA Rm 120 Simon Fraser University Burnaby, BC CANADA V5A 1S6 You can also email pointers to electronic copies, which I will include in the bibliography itself. ---------------------------------------------------------------------- HOW TO GENERATE A BIBLIOGRAPHY FROM THIS FILE Put this file (call it mimetic.bib, say) in a directory. Then, copy the following \cite, \bibliography and \bibliographystyle commands in a latex file in the same directory (call is myfile.tex, say). If you want to use this bib file in addition to one, or more, of your own, simply replace "\bibliography{mimetic}" by "\bibliography{myownbibfile, mimetic}," in which case BibTeX will try to find entries in myownbibfile.bib, and if missing, will look in mimetic.bib. The following, up to \end{document}, is a complete latex file which will produce a formatted bibliography containing all the entries in this file: \documentclass[12pt]{article} \begin{document} \author{Nicolas Robidoux and Stanly Steinberg} \title{Mimetic discretizations bibliography} \maketitle \begin{itemize} \item[1957:] \cite{ 1957Whitney } \item[1966:] \cite{ 1966Branin 1966Yee } \item[1976:] \cite{ 1976Tonti} \item[1977:] \cite{ 1977Samarskii, 1977TontiB} \item[1980:] \cite{ 1980Nedelec } \item[1981:] \cite{ 1981FavorskiiSamarskiiShashkovTishkin } \item[1982:] \cite{ 1982SamarskiiTishkinFavorskiiShashkov, 1982FavorskiiKorshiyaShashkovTishkin } \item[1984:] \cite{ 1984Kotiuga } \item[1986:] \cite{ 1986KreissManteuffelSwartzWendroffWhite, 1986Nedelec } \item[1987:] \cite{ 1987BrezziDouglasDuranFortin, 1987Heinrich } \item[1988:] \cite{ 1988Bossavit, 1988BossavitB, 1988HymanScovel } \item[1990:] \cite{ 1990Dezin } \item[1991:] \cite{ 1991Bossavit, 1991BossavitB, 1991BrezziFortin, 1991VichnevetskyTurner } \item[1992:] \cite{ 1992Bossavit, 1992BossavitB, 1992HymanKnappScovel, 1992Sadiku, 1992VichnevetskyTurner } \item[1993:] \cite{ 1993KunzLuebbers, 1993PalmerShapiro } \item[1995:] \cite{ 1995CastilloHymanShashkovSteinberg, 1995CastilloHymanShashkovSteinbergB, 1995Dezin, 1995Palmer, 1995ShashkovSteinberg } \item[1996:] \cite{ 1996Cessenat, 1996JiangWuPovelli, 1996JolyMetevierRauch, 1996LeVeque, 1996Robidoux, 1996Shashkov, 1996ShashkovSteinberg, 1996Tonti, 1996Weiland } \item[1997:] \cite{ 1997HymanShashkov, 1997HymanShashkovB, 1997HymanShashkovSteinberg, 1997Imagj, 1997Mattiussi, 1997Robidoux } \item[1998:] \cite{ 1998AmmariNedelec, 1998ArbogastDawsonKeenanWheelerYotov, 1998Bossavit, 1998BossavitB, 1998HymanShashkov, 1998HymanShashkovB, 1998MclachlanQuispelRobidoux, 1998MorelRobertsShashkov } \item[1999:] \cite{ 1999ClemensThomaWeilandVanrienen, 1999GradinaruHiptmair, 1999HymanShashkov, 1999HymanShashkovB, 1999KettunenForsmanBossavit, 1999MclachlanQuispelRobidoux, 1999Sinor, 1999Steinberg, 1999TarhasaariKettunenBossavit, 1999TeixeiraChew, 1999TeixeiraChewB } \item[2000:] \cite{ 2000Bennett, 2000Bossavit, 2000CaorsiFernandesRaffetto, 2000ChardShapiro, 2000DeHoopLager, 2000DesbrunMeyerSchoederBarr, 2000MargolinShashkovSmolarkiewicz, 2000Mattiussi, 2000MclachlanRobidoux } \item[2001:] \cite{ 2001BerndtLipnikovMoultonShashkov, 2001BessonovSong, 2001BluckWalkerOrdovas, 2001BohnerCastillo, 2001Bossavit, 2001BuffaHiptmairVonpetersdorffSchwab, 2001Buksas, 2001CastilloHymanShashkovSteinberg, 2001ClemensWeiland, 2001GrossKotiuga, 2001GrossKotiugaB, 2001Hiptmair, 2001HiptmairB, 2001HiptmairC, 2001HiptmairD, 2001HymanCampbellShashkov, 2001HymanMorelShashkovSteinberg, 2001HymanShashkov, 2001HymanShashkovSteinberg, 2001KarasozenTsybulin, 2001KitsonMclachlanRobidoux, 2001KoleFiggeDeRaedt, 2001LiskaGanzhaZenger, 2001Marrone, 2001Mattiussi, 2001MeyerDesbrunSchroederBarr, 2001MorelHallShashkov, 2001Puska, 2001Samarskii, 2001Seiler, 2001TarhasaariKettunen, 2001Teixeira, 2001TeixeiraB, 2001Tonti, 2001Vanrienen } \item[2002:] \cite{ 2002Arnold, 2002DeHoopLagerJorna, 2002EstepTavener, 2002Hiptmair, 2002HymanMorelShashkovSteinberg, 2002HymanSteinberg, 2002Mattiussi, 2002Robidoux, 2002RobidouxSteinberg, 2002Steinberg } \end{itemize} \bibliography{mimetic} \bibliographystyle{alpha} \end{document} (Of course, if you are writing an article for a SIAM journal, you should use "siam" instead of "alpha," etc.) Then, issue the commands (this is for Unix) latex myfile bibtex myfile latex myfile latex myfile (You need to pass the file through latex a few times to get the bibliography and the keys right.) The dvi file myfile.dvi should now contain a formatted bibliography with the above entries. Enjoy! ---------------------------------------------------------------------- @BOOK{1957Whitney, AUTHOR = {Hassler Whitney}, TITLE = {Geometric integration theory}, PUBLISHER = {Princeton University Press}, ADDRESS = {Princeton, N. J.}, YEAR = {1957}, PAGES = {xv+387}, MRCLASS = {53.0X}, MRNUMBER = {19,309c}, MRREVIEWER = {H. Samelson}, } @InProceedings{1966Branin, AUTHOR = {F. H. {Branin, Jr.}}, TITLE = {The algebraic-topological basis for network analogies and for vector calculus}, BOOKTITLE = {{S}ymposium on {G}eneralized {N}etworks (12--14 {A}pril 1966)}, PAGES = {453--491}, YEAR = {1966}, ORGANIZATION = {Polytechnic Institute of Brooklyn}, } @ARTICLE{1966Yee, AUTHOR = {K. S. Yee}, TITLE = {Numerical Solution of Initial Boundary Value Problems Involving {M}axwell's Equations in Isotropic Media}, JOURNAL = {{I}{E}{E}{E} {T}ransactions of {A}ntennas and {P}ropagation}, YEAR = {1966}, VOLUME = {AP-14}, NUMBER = {3}, PAGES = {302--307}, } @ARTICLE{1976Tonti, AUTHOR = {Enzo Tonti}, TITLE = {Sulla struttura formale delle teorie fisiche}, JOURNAL = {Rend. Sem. Mat. Fis. Milano}, VOLUME = {46}, YEAR = {1976}, PAGES = {163--257 (1978)}, MRCLASS = {83.58 (02G99)}, MRNUMBER = {58 \#14974}, MRREVIEWER = {George S. Whiston}, } @BOOK{1977Samarskii, AUTHOR = {A. A. Samarski\u{\i}}, TITLE = {Teoriya raznostnykh skhem}, PUBLISHER = {Izdat. ``Nauka'', Moscow}, YEAR = {1977}, PAGES = {656}, MRCLASS = {65-01 (65MXX 65NXX 69.00)}, MRNUMBER = {58 \#3288}, MRREVIEWER = {M. Zlamal}, } @ARTICLE{1977TontiB, AUTHOR = {Enzo Tonti}, TITLE = {The reason for analogies between physical theories}, JOURNAL = {Appl. Math. Modelling}, VOLUME = {1}, YEAR = {1976/77}, NUMBER = {1}, PAGES = {37--50}, MRCLASS = {02A05 (00A25)}, MRNUMBER = {58 \#5001}, } @ARTICLE{1980Nedelec, AUTHOR = {J.-C. N{\'e}d{\'e}lec}, TITLE = {Mixed finite elements in ${\bf {R}}\sp{3}$}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {35}, YEAR = {1980}, NUMBER = {3}, PAGES = {315--341}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65N30}, MRNUMBER = {81k:65125}, MRREVIEWER = {P. G. Ciarlet}, } @ARTICLE{1981FavorskiiSamarskiiShashkovTishkin, AUTHOR = {A. Favorskii and A. Samarskii and Mikhail J. Shashkov and V. Tishkin}, TITLE = {Operational Finite-Difference Schemes}, JOURNAL = {Differential Equations}, VOLUME = {17}, YEAR = {1981}, PAGES = {854--862}, } @ARTICLE{1982SamarskiiTishkinFavorskiiShashkov, AUTHOR = {A. A. Samarski\u{\i} and V. F. Tishkin and A. P. Favorski\u{\i} and M. Yu. Shashkov}, TITLE = {Use of the support operator method for constructing difference analogues of operations of tensor analysis}, JOURNAL = {Differentsial nye Uravneniya}, FJOURNAL = {Differentsial nye Uravneniya}, VOLUME = 18, YEAR = 1982, NUMBER = 7, PAGES = {1251--1256, 1287}, ISSN = {0374-0641}, MRCLASS = {65N05}, MRNUMBER = {83k:65072}, MRREVIEWER = {Ra\u{\i} cho Lazarov}, NOTE = {English translation: Differential Equations 18 (1982), no. 7, 881--885.}, } @ARTICLE{1982FavorskiiKorshiyaShashkovTishkin, AUTHOR = {A. Favorskii and T. Korshiya and Mikhail J. Shashkov and V. Tishkin}, TITLE = {Variational Approach to The Construction of Finite-Difference Schemes for The Diffusion Equations for Magnetic Field}, JOURNAL = {Differential Equations}, VOLUME = {18}, YEAR = {1982}, NUMBER = {7}, PAGES = {863--872} } @PHDTHESIS{1984Kotiuga, AUTHOR = {P.R. Kotiuga}, TITLE = {{H}odge decompositions and computational electromagnetics}, SCHOOL = {Department of Electrical Engineering, McGill University}, YEAR = 1984, ADDRESS = {Montr\'eal}, } @ARTICLE{1986KreissManteuffelSwartzWendroffWhite, AUTHOR = {H.-O. Kreiss and T. A. Manteuffel and B. Swartz and B. Wendroff and A. B. White, Jr.}, TITLE = {Supra-convergent schemes on irregular grids}, JOURNAL = {Math. Comp.}, FJOURNAL = {Mathematics of Computation}, VOLUME = {47}, YEAR = {1986}, NUMBER = {176}, PAGES = {537--554}, ISSN = {0025-5718}, CODEN = {MCMPAF}, MRCLASS = {65L05 (40A30 65D25 65L10)}, MRNUMBER = {88b:65082}, MRREVIEWER = {Randall J. LeVeque}, } @ARTICLE{1986Nedelec, AUTHOR = {J.-C. N{\'e}d{\'e}lec}, TITLE = {A new family of mixed finite elements in ${\bf {R}}\sp 3$}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {50}, YEAR = {1986}, NUMBER = {1}, PAGES = {57--81}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65N30}, MRNUMBER = {88e:65145}, } @ARTICLE{1987BrezziDouglasDuranFortin, AUTHOR = {Franco Brezzi and Jim {Douglas, Jr.}, and Ricardo Dur{\'a}n and Michel Fortin}, TITLE = {Mixed finite elements for second order elliptic problems in three variables}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {51}, YEAR = {1987}, NUMBER = {2}, PAGES = {237--250}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {65N30}, MRNUMBER = {88f:65190}, MRREVIEWER = {Jaroslaw Jelen}, } @BOOK{1987Heinrich, AUTHOR = {Bernd Heinrich}, TITLE = {Finite difference methods on irregular networks}, SERIES = {Internationale Schriftenreihe zur Numerischen Mathematik [International Series of Numerical Mathematics]}, VOLUME = {82}, PUBLISHER = {Birkh\"auser Verlag}, ADDRESS = {Basel}, YEAR = {1987}, PAGES = {206}, ISBN = {3-7643-1880-5}, MRCLASS = {65N06}, MRNUMBER = {91d:65145}, MRREVIEWER = {M. Zl{\'a}mal}, NOTE = {A generalized approach to second order elliptic problems.}, } @INCOLLECTION{1988Bossavit, AUTHOR = {Alain Bossavit}, TITLE = {Mixed finite elements and the complex of {W}hitney forms}, BOOKTITLE = {The mathematics of finite elements and applications, VI (Uxbridge, 1987)}, PAGES = {137--144}, PUBLISHER = {Academic Press}, ADDRESS = {London}, YEAR = {1988}, MRCLASS = {58A99 (65N30)}, MRNUMBER = {89k:58028}, MRREVIEWER = {A. P. Stone}, } @ARTICLE{1988BossavitB, AUTHOR = {Alain Bossavit}, TITLE = {{W}hitney forms: A new class of finite elements for three-dimensional computations in electromagnetics}, JOURNAL = {{I}{E}{E} Proc. {A}}, VOLUME = {135}, PAGES = {493--500}, YEAR = {1988}, } @TECHREPORT{1988HymanScovel, AUTHOR = {James M. Hyman and J. C. Scovel}, TITLE = {Deriving mimetic difference approximations to differential operators using algebraic topology}, INSTITUTION = {Los Alamos National Laboratory}, YEAR = 1988, PAGES = {iii+31}, ADDRESS = {Los Alamos, NM 87545}, } @Book{1990Dezin, AUTHOR = {Dezin, A. A.}, TITLE = {Mnogomernyi analiz i diskretnye modeli}, NOTE = {In Russian. With an English summary}, PUBLISHER = {``Nauka''}, ADDRESS = {Moscow}, YEAR = {1990}, PAGES = {240}, ISBN = {5-02-014208-5}, MRCLASS = {00A73 (53-02 58-02)}, MRNUMBER = {94d:00010}, } @ARTICLE{1991Bossavit, AUTHOR = {Alain Bossavit}, TITLE = {Differential forms and the computation of fields and forces in electromagnetism}, JOURNAL = {European J. Mech. B Fluids}, FJOURNAL = {European Journal of Mechanics. B Fluids}, VOLUME = 10, YEAR = 1991, NUMBER = 5, PAGES = {474--488}, ISSN = {0997-7546}, CODEN = {EJBFEV}, MRCLASS = {78A25 (58A10 78-08)}, MRNUMBER = {92m:78004}, MRREVIEWER = {A. P. Stone}, } @ARTICLE{1991BossavitB, AUTHOR = {Bossavit, Alain}, TITLE = {Mixed methods and the marriage between ``mixed'' finite elements and boundary elements}, JOURNAL = {Numer. Methods Partial Differential Equations}, FJOURNAL = {Numerical Methods for Partial Differential Equations. An International Journal}, VOLUME = {7}, YEAR = {1991}, NUMBER = {4}, PAGES = {347--362}, ISSN = {0749-159X}, MRCLASS = {65N30 (65N38 78A30)}, MRNUMBER = {92h:65163}, } @BOOK{1991BrezziFortin, AUTHOR = {Franco Brezzi and Michel Fortin}, TITLE = {Mixed and hybrid finite element methods}, SERIES = {Springer Series in Computational Mathematics}, VOLUME = {15}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1991}, PAGES = {x+350}, ISBN = {0-387-97582-9}, MRCLASS = {65N30 (65-02 73V05 76M10)}, MRNUMBER = {92d:65187}, MRREVIEWER = {Lubor Malina}, } @ARTICLE{1991VichnevetskyTurner, AUTHOR = {R. Vichnevetsky and L. H. Turner}, TITLE = {Spurious scattering from discontinuously stretching grids in computational fluid dynamics}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {8}, YEAR = {1991}, NUMBER = {3}, PAGES = {289--299}, ISSN = {0168-9274}, CODEN = {ANMAEL}, MRCLASS = {76M20 (65M50)}, MRNUMBER = {92g:76061}, } @ARTICLE{1992Bossavit, AUTHOR = {Alain Bossavit}, TITLE = {On local computation of the force field in deformable bodies}, JOURNAL = {Applied Electromagnetics in Materials}, YEAR = {1992}, VOLUME = {2}, NUMBER = {4}, PAGES = {333--343}, } @ARTICLE{1992BossavitB, AUTHOR = {Alain Bossavit}, TITLE = {Edge-element Computation of The Force Field in Deformable Bodies}, JOURNAL = {{I}{E}{E}{E} Trans. Magnetics}, YEAR = {1992}, VOLUME = {28}, NUMBER = {2}, PAGES = {1263--1266}, } @ARTICLE{1992HymanKnappScovel, AUTHOR = {James M. Hyman and Robert J. Knapp and James C. Scovel}, TITLE = {High order finite volume approximations of differential operators on nonuniform grids}, NOTE = {Experimental mathematics: computational issues in nonlinear science (Los Alamos, NM, 1991)}, JOURNAL = {Phys. D}, FJOURNAL = {Physica D. Nonlinear Phenomena}, VOLUME = {60}, YEAR = {1992}, NUMBER = {1-4}, PAGES = {112--138}, ISSN = {0167-2789}, CODEN = {PDNPDT}, MRCLASS = {65N30}, MRNUMBER = {93i:65110}, } @BOOK{1992Sadiku, AUTHOR = {Matthew N.O. Sadiku}, TITLE = {Numerical Techniques in Electromagnetics}, PUBLISHER = {CRC Press}, YEAR = {1992}, ADDRESS = {Boca Raton}, } @INPROCEEDINGS{1992VichnevetskyTurner, AUTHOR = {R. Vichnevetsky and L.H. Turner}, TITLE = {Singular Scattering in Discontinuously Stretching Grids for the Wave Equation}, BOOKTITLE = {Advances in Computer Methods for Partial Differential Equations VII}, YEAR = {1992}, PAGES = {761--769}, PUBLISHER = {IMACS}, } @BOOK{1993KunzLuebbers, AUTHOR = {Karl S. Kunz and Raymond J. Luebbers}, TITLE = {The Finite Difference Time Domain Method for Electromagnetics}, PUBLISHER = {CRC Press}, YEAR = {1993}, ADDRESS = {Boca Raton}, } @ARTICLE{1993PalmerShapiro, AUTHOR = {Richard S. Palmer and Vadim Shapiro}, TITLE = {Chain Models of Physical Behavior for Engineering Analysis and Design}, JOURNAL = {Research in Engineering Design}, YEAR = {1993}, VOLUME = {5}, PAGES = {161--184}, } @INPROCEEDINGS{1995CastilloHymanShashkovSteinberg, AUTHOR = {Jose Castillo and James M. Hyman and Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {High-Order Mimetic Finite Difference Methods on Nonuniform Grids}, BOOKTITLE = {ICOSAHOM-95, Proc. of the Third International Conference on Spectral and High Order Methods, Houston, Texas, 5-9 June 1995}, YEAR = {1995}, EDITOR = {A.V. Ilin and L. R. Scott}, PAGES = {347--361}, PUBLISHER = {Special Issue of Houston Journal of Mathematics}, } @ARTICLE{1995CastilloHymanShashkovSteinbergB, AUTHOR = {Jose Castillo and James M. Hyman and Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {The Sensitivity and Accuracy of Fourth Order Finite-Difference Schemes on Nonuniform Grids in One Dimension}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {30}, YEAR = {1995}, NUMBER = {8}, PAGES = {41--55}, ISSN = {0898-1221}, CODEN = {CMAPDK}, MRCLASS = {65D25 (65P05)}, MRNUMBER = {96f:65025}, } @BOOK{1995Dezin, AUTHOR = {Aleksei A. Dezin}, TITLE = {Multidimensional analysis and discrete models}, NOTE = {Translated from the Russian by Irene Aleksanova}, PUBLISHER = {CRC Press}, ADDRESS = {Boca Raton, FL}, YEAR = {1995}, PAGES = {viii+244}, ISBN = {0-8493-9425-2}, MRCLASS = {00A73 (53-02 58-02 81P99)}, MRNUMBER = {98b:00015}, MRREVIEWER = {Jules Beckers}, } @Article{1995Palmer, AUTHOR = {Richard S. Palmer}, TITLE = {Chain models and finite element analysis: an executable {CHAINS} formulation of plane stress}, NOTE = {Grid generation, finite elements, and geometric design}, JOURNAL = {Comput. Aided Geom. Design}, FJOURNAL = {Computer Aided Geometric Design}, VOLUME = {12}, YEAR = {1995}, NUMBER = {7}, PAGES = {733--770}, ISSN = {0167-8396}, CODEN = {CAGDEX}, MRCLASS = {65N30 (65D17)}, MRNUMBER = {1 365 106}, } @ARTICLE{1995ShashkovSteinberg, AUTHOR = {Mikhail Shashkov and Stanly Steinberg}, TITLE = {Support-operator finite-difference algorithms for general elliptic problems}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {118}, YEAR = {1995}, NUMBER = {1}, PAGES = {131--151}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {65N06}, MRNUMBER = {95m:65181}, } @BOOK{1996Cessenat, AUTHOR = {Michel Cessenat}, TITLE = {Mathematical methods in electromagnetism}, SERIES = {Series on Advances in Mathematics for Applied Sciences}, VOLUME = {41}, NOTE = {Linear theory and applications}, PUBLISHER = {World Scientific Publishing Co. Inc.}, ADDRESS = {River Edge, NJ}, YEAR = {1996}, PAGES = {xiv+376}, ISBN = {981-02-2467-2}, MRCLASS = {78-02 (78A25)}, MRNUMBER = {97j:78001}, MRREVIEWER = {Ll. G. Chambers}, } @ARTICLE{1996JiangWuPovelli, AUTHOR = {B. N. Jiang and J. Wu and L.A. Povelli}, TITLE = {The origin of spurious solutions in computational electrodynamics}, JOURNAL = {Journal of Computational Physics}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {125}, YEAR = {1996}, PAGES = {104--123}, } @ARTICLE{1996JolyMetevierRauch, AUTHOR = {J.L. Joly and G. Metevier and J. Rauch}, TITLE = {Global solvability of the anharmonic oscillator model from nonlinear optics}, JOURNAL = {SIAM J. Math. Anal.}, FJOURNAL = {SIAM Journal on Mathematical Analysis}, VOLUME = {27}, YEAR = {1996}, NUMBER = {4}, PAGES = {905--913}, ISSN = {0036-1410}, CODEN = {SJMAAH}, MRCLASS = {78A40 (35Q60)}, MRNUMBER = {97f:78023}, MRREVIEWER = {V. H. Weston}, } @ARTICLE{1996LeVeque, AUTHOR = {R.J. LeVeque}, TITLE = {High-resolution Conservative Algorithms for Advection in Incompressible Flow}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {33}, YEAR = {1996}, NUMBER = {2}, PAGES = {627--665}, ISSN = {0036-1429}, CODEN = {SJNAAM}, MRCLASS = {76M20 (65M99)}, MRNUMBER = {98b:76049}, MRREVIEWER = {Jian Guo Liu}, } @INPROCEEDINGS{1996Robidoux, AUTHOR = {Nicolas Robidoux}, TITLE = {A New Method of Construction of Adjoint Gradients and Divergences on Logically Rectangular Smooth Grids}, BOOKTITLE = {Finite Volumes for Complex Applications: Problems and Perspectives, First International Symposium, July 15--18, 1996, {R}ouen, {F}rance}, YEAR = 1996, EDITOR = {Benkaldoun, F. and Vilsmeier, R.}, PAGES = {261--272}, PUBLISHER = {Editions Herm\`{e}s}, ADDRESS = {Paris}, URL = {http://citeseer.nj.nec.com/468699.html or www.math.sfu.ca/~nrobidou/public_html/prints/rouen/rouen.ps.gz}, } @BOOK{1996Shashkov, AUTHOR = {Mikhail J. Shashkov}, TITLE = {Conservative finite-difference methods on general grids}, NOTE = {With 1 IBM-PC floppy disk (3.5 inch; HD)}, PUBLISHER = {CRC Press}, ADDRESS = {Boca Raton, FL}, YEAR = 1996, PAGES = {xviii+359}, ISBN = {0-8493-7375-1}, MRCLASS = {65M06 (65-02 65N06 76M20 76N15)}, MRNUMBER = {97m:65150}, MRREVIEWER = {Dietmar Kr{\"o}ner}, } @ARTICLE{1996ShashkovSteinberg, AUTHOR = {Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {Solving diffusion equations with rough coefficients in rough grids}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {129}, YEAR = {1996}, NUMBER = {2}, PAGES = {383--405}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {76M20}, MRNUMBER = {97g:76066}, } @InCollection{1996Tonti, author = {Enzo Tonti}, title = {On the geometrical structure of electromagnetism}, booktitle = {Gravitation, Electromagnetism and Geometrical Structures}, pages = {281--308}, publisher = {Pitagora}, year = {1996}, editor = {G. Ferraese}, address = {Bologna}, } @ARTICLE{1996Weiland, AUTHOR = {Thomas Weiland}, TITLE = {Time domain electromagnetic field computation with finite difference methods}, JOURNAL = {Int. J. Num. Modelling}, FJOURNAL = {International Journal of Numerical Modelling: Electronic Networks, Devices and Fields}, YEAR = {1996}, MONTH = {July/August}, VOLUME = {9}, NUMBER = {4}, PAGES = {295--319}, } @ARTICLE{1997HymanShashkov, AUTHOR = {James M. Hyman and Mikhail J. Shashkov}, TITLE = {Natural discretizations for the divergence, gradient, and curl on logically rectangular grids}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {33}, YEAR = {1997}, NUMBER = {4}, PAGES = {81--104}, ISSN = {0898-1221}, CODEN = {CMAPDK}, MRCLASS = {39A12 (39A70 65D25 65L12)}, MRNUMBER = {98i:39004}, MRREVIEWER = {Philip Huddleston}, } @ARTICLE{1997HymanShashkovB, AUTHOR = {James M. Hyman and Mikhail J. Shashkov}, TITLE = {Adjoint operators for the natural discretizations of the divergence, gradient and curl on logically rectangular grids}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {25}, YEAR = {1997}, NUMBER = {4}, PAGES = {413--442}, ISSN = {0168-9274}, CODEN = {ANMAEL}, MRCLASS = {39A12 (65C20 65N06)}, MRNUMBER = {99c:39018}, MRREVIEWER = {Sui Yang Chen}, } @ARTICLE{1997HymanShashkovSteinberg, AUTHOR = {James M. Hyman and Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {132}, YEAR = {1997}, NUMBER = {1}, PAGES = {130--148}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {65N06 (76M20 80-08)}, MRNUMBER = {98a:65151}, MRREVIEWER = {Leonid K. Antanovski{\u\i}}, } @UNPUBLISHED{1997Imagj, AUTHOR = {{I}mage{J} group}, TITLE = {{I}mage{J}: {I}mage {P}rocessing in {J}ava}, URL = {http://rsb.info.nih.gov/ij/}, } @ARTICLE{1997Mattiussi, AUTHOR = {Claudio Mattiussi}, TITLE = {An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {133}, YEAR = {1997}, NUMBER = {2}, PAGES = {289--309}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {65M60 (65N30)}, MRNUMBER = {1 447 090}, } @TECHREPORT{1997Robidoux, AUTHOR = {Nicolas Robidoux}, TITLE = {Natural Finite volume Discretizations of the Gradient, Divergence, Laplacian, Diffusion tensor and Advective Term on Grids with Quadrilateral Cells}, URL = "citeseer.nj.nec.com/robidoux97natural.html", YEAR = 1997, PAGES = 83, INSTITUTION = {CiteSeer ({N}{E}{C} Research Index)}, NOTE = {Unfinished thesis draft.}, URL = {http://citeseer.nj.nec.com/robidoux97natural.html or http://www.math.sfu.ca/~nrobidou/public_html/prints/oldthesis/oldthes.ps}, } @INCOLLECTION{1998AmmariNedelec, AUTHOR = {Habib Ammari and Jean-Claude N{\'e}d{\'e}lec}, TITLE = {Couplage \'el\'ements finis/\'equations int\'egrales pour la r\'esolution des \'equations de {M}axwell en milieu h\'et\'erog\`ene}, BOOKTITLE = {\'Equations aux d\'eriv\'ees partielles et applications}, PAGES = {19--33}, PUBLISHER = {Gauthier-Villars}, ADDRESS = {\'Ed. Sci. M\'ed. Elsevier, Paris}, YEAR = {1998}, MRCLASS = {65N30 (35Q60 45L05 78-08 78A25)}, MRNUMBER = {99i:65122}, MRREVIEWER = {P. Rochus}, } @ARTICLE{1998ArbogastDawsonKeenanWheelerYotov, AUTHOR = {Todd Arbogast and Clint N. Dawson and Philip T. Keenan and Mary F. Wheeler and Ivan Yotov}, TITLE = {Enhanced cell-centered finite differences for elliptic equations on general geometry}, JOURNAL = {SIAM J. Sci. Comput.}, FJOURNAL = {SIAM Journal on Scientific Computing}, VOLUME = {19}, YEAR = {1998}, NUMBER = {2}, PAGES = {404--425 (electronic)}, ISSN = {1095-7197}, MRCLASS = {65N30}, MRNUMBER = {99j:65193}, MRREVIEWER = {S. Galanis}, } @BOOK{1998Bossavit, AUTHOR = {Alain Bossavit}, TITLE = {Computational electromagnetism}, PUBLISHER = {Academic Press Inc.}, ADDRESS = {San Diego, CA}, YEAR = {1998}, PAGES = {xx+352}, ISBN = {0-12-118710-1}, MRCLASS = {78-08 (65N99 78-02 78A30)}, MRNUMBER = {99m:78001}, MRREVIEWER = {Pierre Hillion}, } @Article{1998BossavitB, author = {Alain Bossavit}, TITLE = {How weak is the ``weak solution'' in finite element methods?}, journal = {{I}{E}{E}{E} Trans. Magnetics}, year = 1998, volume = 34, pages = {2429--2432}, } @ARTICLE{1998HymanShashkov, AUTHOR = {James M. Hyman and Mikhail J. Shashkov}, TITLE = {The Approximation of Boundary Conditions for Mimetic Finite Difference Methods}, JOURNAL = {Computers \& Mathematics with Applications}, VOLUME = {36}, YEAR = {1998}, PAGES = {79--99}, } @INPROCEEDINGS{1998HymanShashkovB, AUTHOR = {James M. Hyman and Mikhail J. Shashkov}, TITLE = {Mimetic discretizations for {M}axwell's equations and equations of magnetic diffusion}, BOOKTITLE = {Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, 1998}, YEAR = {1998}, EDITOR = {J. A. DeSanto}, PAGES = {561--563}, PUBLISHER = {SIAM}, } @ARTICLE{1998MclachlanQuispelRobidoux, AUTHOR = {Robert I. McLachlan and G. R. W. Quispel and Nicolas Robidoux}, TITLE = {Unified approach to {H}amiltonian systems, {P}oisson systems, gradient systems, and systems with {L}yapunov functions or first integrals}, JOURNAL = {Phys. Rev. Lett.}, FJOURNAL = {Physical Review Letters}, VOLUME = {81}, YEAR = {1998}, NUMBER = {12}, PAGES = {2399--2403}, ISSN = {0031-9007}, CODEN = {PRLTAO}, MRCLASS = {58F05 (34A34)}, MRNUMBER = {99f:58079}, URL = {http://www.massey.ac.nz/~rmclachl//prl98.pdf}, } @ARTICLE{1998MorelRobertsShashkov, AUTHOR = {J. E. Morel and R. M. Roberts and Mikhail J. Shashkov}, TITLE = {A Local Support-Operators Diffusion Discretization Scheme}, JOURNAL = {Journal of Computational Physics}, VOLUME = {144}, YEAR = {1998}, PAGES = {17--51}, } @ARTICLE{1999ClemensThomaWeilandVanrienen, AUTHOR = {Markus Clemens and Peter Thoma and Thomas Weiland and Ursula van Rienen}, TITLE = {Computational electromagnetic-field calculation with the finite-integration method}, JOURNAL = {Surv. Math. Ind.}, FJOURNAL = {Surveys on Mathematics for Industry}, YEAR = {1999}, VOLUME = {8}, PAGES = {213--232}, } @ARTICLE{1999GradinaruHiptmair, AUTHOR = {V. Gradinaru and R. Hiptmair}, TITLE = {{W}hitney elements on pyramids}, JOURNAL = {Electron. Trans. Numer. Anal.}, FJOURNAL = {Electronic Transactions on Numerical Analysis}, VOLUME = {8}, YEAR = {1999}, PAGES = {154--168 (electronic)}, ISSN = {1068-9613}, MRCLASS = {65N30 (65D15 78M10)}, MRNUMBER = {2001f:65134}, MRREVIEWER = {Do Young Kwak}, } @ARTICLE{1999HymanShashkov, AUTHOR = {James M. Hyman and Mikhail J. Shashkov}, TITLE = {The orthogonal decomposition theorems for mimetic finite difference methods}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {36}, YEAR = {1999}, NUMBER = {3}, PAGES = {788--818 (electronic)}, ISSN = {1095-7170}, MRCLASS = {65N06}, MRNUMBER = {2000c:65094}, MRREVIEWER = {Patrick M. Knupp}, } @ARTICLE{1999HymanShashkovB, AUTHOR = {James M. Hyman and Mikhail J. Shashkov}, TITLE = {Mimetic discretizations for {M}axwell's equations}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {151}, YEAR = {1999}, NUMBER = {2}, PAGES = {881--909}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {78M10}, MRNUMBER = {2000a:78038}, } @ARTICLE{1999KettunenForsmanBossavit, AUTHOR = {Lauri Kettunen and Kimmo Forsman and Alain Bossavit}, TITLE = {Gauging in {W}hitney spaces}, JOURNAL = {{I}{E}{E}{E} Trans. Magnetics}, YEAR = {1999}, VOLUME = {35}, NUMBER = {3}, PAGES = {1466--1469}, MONTH = {May} } @ARTICLE{1999MclachlanQuispelRobidoux, AUTHOR = {Robert I. McLachlan and G. R. W. Quispel and Nicolas Robidoux}, TITLE = {Geometric integration using discrete gradients}, JOURNAL = {R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci.}, FJOURNAL = {The Royal Society of London. Philosophical Transactions. Series A. Mathematical, Physical and Engineering Sciences}, VOLUME = {357}, YEAR = {1999}, NUMBER = {1754}, PAGES = {1021--1045}, ISSN = {1364-503X}, MRCLASS = {34A45 (37M15 65L99 70-08)}, MRNUMBER = {2000f:34021}, MRREVIEWER = {Steve Shkoller}, URL = {http://citeseer.nj.nec.com/mclachlan98geometric.html}, } @MISC{1999Sinor, AUTHOR = {M. Sinor}, TITLE = {Simulation and visualization of elastodynamical waves in general nonhomogeneous matter}, HOWPUBLISHED = {{\tt http://www-troja.fjfi.cvut.cz/\~{}sinor/r/lisa}}, YEAR = {1999}, URL = {http://www-troja.fjfi.cvut.cz/~sinor/r/lisa}, } @INPROCEEDINGS{1999Steinberg, AUTHOR = {S. Steinberg}, TITLE = {The Accuracy of Numerical Models For Continuum Problems}, BOOKTITLE = {Error Control and Adaptivity in Scientific Computing}, YEAR = {1999}, EDITOR = {H. Bulgak and C. Zenger}, PAGES = {299-323}, PUBLISHER = {NATO Science Series}, NOTE = {Series C: Mathematical and Physical Sciences, 536}, } @ARTICLE{1999TarhasaariKettunenBossavit, AUTHOR = {T. Tarhasaari and L. Kettunen and Alain Bossavit}, TITLE = {Some realizations of a discrete {H}odge operator: A reinterpretation of finite element techniques}, JOURNAL = {{I}{E}{E}{E} Trans. Magn.}, VOLUME = 35, PAGES = {1494--1497}, YEAR = 1999, } @ARTICLE{1999TeixeiraChew, AUTHOR = {F. L. Teixeira and W. C. Chew}, TITLE = {{Differential forms, metrics, and the reflectionless absorption of electromagnetic waves}}, JOURNAL = {J. Electromagn. Waves Applicat.}, VOLUME = 13, NUMBER = 5, PAGES = {665--686}, YEAR = 1999, } @ARTICLE{1999TeixeiraChewB, AUTHOR = {F. L. Teixeira and W. C. Chew}, TITLE = {Lattice electromagnetic theory from a topological viewpoint}, JOURNAL = {J. Math. Phys.}, FJOURNAL = {Journal of Mathematical Physics}, VOLUME = {40}, YEAR = {1999}, NUMBER = {1}, PAGES = {169--187}, ISSN = {0022-2488}, CODEN = {JMAPAQ}, MRCLASS = {78A25 (58A10)}, MRNUMBER = {2001a:78013} } @PHDTHESIS{2000Bennett, AUTHOR = {Paul M. Bennett}, TITLE = {Parallel Numerical Integration of Maxwell's Full-Vector Equations in Nonlinear Focusing Media}, SCHOOL = {University of New Mexico}, ADDRESS = {Albuquerque, NM}, YEAR = 2000, } @INCOLLECTION{2000Bossavit, AUTHOR = {Alain Bossavit}, TITLE = {The discrete {H}odge operator in electromagnetic wave propagation problems}, BOOKTITLE = {Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000)}, PAGES = {753--759}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia, PA}, YEAR = {2000}, MRCLASS = {78M20 (35Q60 65N22)}, MRNUMBER = {1 785 982} } @ARTICLE{2000CaorsiFernandesRaffetto, AUTHOR = {Salvatore Caorsi and Paolo Fernandes and Mirco Raffetto}, TITLE = {On the convergence of {G}alerkin finite element approximations of electromagnetic eigenproblems}, JOURNAL = {SIAM J. Numer. Anal.}, FJOURNAL = {SIAM Journal on Numerical Analysis}, VOLUME = {38}, YEAR = {2000}, NUMBER = {2}, PAGES = {580--607 (electronic)}, ISSN = {1095-7170}, MRCLASS = {65N25 (65N30 78M10)}, MRNUMBER = {2001e:65172}, MRREVIEWER = {Ma{\l}gorzata Peszy{\'n}ska}, } @ARTICLE{2000ChardShapiro, AUTHOR = {Jeffrey A. Chard and Vadim Shapiro}, TITLE = {A multivector data structure for differential forms and equations}, JOURNAL = {Math. Comput. Simulation}, FJOURNAL = {Mathematics and Computers in Simulation}, VOLUME = {54}, YEAR = {2000}, NUMBER = {1-3}, PAGES = {33--64}, ISSN = {0378-4754}, CODEN = {MCSIDR}, MRCLASS = {65Y20 (68W30)}, MRNUMBER = {2001j:65204}, } @ARTICLE{2000DeHoopLager, AUTHOR = {Adrianus T. de Hoop and Ioan E. Lager}, TITLE = {Domain-Integrated Field Approach to static magnetic field computation---Application to some two-dimensional configurations}, JOURNAL = {{I}{E}{E}{E} Trans. Magnetics}, YEAR = {2000}, VOLUME = {36}, NUMBER = {4}, PAGES = {654--658} } @ARTICLE{2000DesbrunMeyerSchoederBarr, AUTHOR = {Mathieu Desbrun and Mark Meyer and Peter Schroeder and Alan H. Barr}, TITLE = {Anisotropic Feature-Preserving Denoising of Bivariate Data}, JOURNAL = {Graphics Interface 2000}, YEAR = {2000}, PAGES = {00--00}, } @ARTICLE{2000MargolinShashkovSmolarkiewicz, AUTHOR = {L. Margolin and Mikhail J. Shashkov and P. Smolarkiewicz}, TITLE = {A Discrete Operator Calculus for Finite Difference Approximations}, JOURNAL = {Comput. Methods Appl. Mech. Engrg.}, VOLUME = {187}, YEAR = {2000}, PAGES = {365--383}, } @ARTICLE{2000Mattiussi, AUTHOR = {Claudio Mattiussi}, TITLE = {The finite volume, finite element, and finite difference methods as numerical methods for physical field problems}, JOURNAL = {Advances in Imaging and Electron Physics}, VOLUME = {113}, YEAR = {2000}, PAGES = {1--146}, } @INCOLLECTION{2000MclachlanRobidoux, AUTHOR = {Robert I. McLachlan and Nicolas Robidoux}, TITLE = {Antisymmetry, pseudospectral methods, and conservative {P}{D}{E}s}, BOOKTITLE = {International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999)}, PAGES = {994--999}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {2000}, MRCLASS = {37K05 (35L65)}, MRNUMBER = {1 870 274}, URL = {http://citeseer.nj.nec.com/498930.html}, } @ARTICLE{2001BerndtLipnikovMoultonShashkov, AUTHOR = {Markus Berndt and Konstantin Lipnikov and J. David Moulton and Mikhail J. Shashkov}, TITLE = {Convergence of mimetic finite difference discretizations of the diffusion equation}, JOURNAL = {East-West J. Numer. Math.}, FJOURNAL = {East-West Journal of Numerical Mathematics}, VOLUME = {9}, YEAR = {2001}, NUMBER = {4}, PAGES = {265--284}, ISSN = {0928-0200}, MRCLASS = {65N06 (65N30)}, MRNUMBER = {2003a:65085}, MRREVIEWER = {Hans-Peter Helfrich}, } @ARTICLE{2001BessonovSong, AUTHOR = {N.M. Bessonov and D.J. Song}, TITLE = {Application of vector calculus to numerical simulation of continuum mechanics problems}, JOURNAL = {Journal of Computational Physics}, VOLUME = {167}, YEAR = {2001}, PAGES = {22--38}, } @UNPUBLISHED{2001BluckWalkerOrdovas, AUTHOR = {M. J. Bluck and Simon P. Walker and Roland Ordovas}, TITLE = {Time Domain Finite Element Methods for EM Modelling}, BOOKTITLE = {European Congress on Computational Methods in Applied Sciences and Engineering}, YEAR = {2001}, NOTE = {Preprint: See {\tt http://www.me.ic.ac.uk/mechanics/staff/mjb.html}}, URL = {http://www.me.ic.ac.uk/mechanics/staff/mjb.html}, } @ARTICLE{2001BohnerCastillo, AUTHOR = {M. Bohner and Jose Castillo}, TITLE = {Mimetic methods on measure chains}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {42}, YEAR = {2001}, NUMBER = {3-5}, PAGES = {705--710}, ISSN = {0898-1221}, CODEN = {CMAPDK}, MRCLASS = {34A99 (65Q05)}, MRNUMBER = {2002d:34021}, MRREVIEWER = {E. Thandapani}, NOTE = {Advances in difference equations, III.}, } @INCOLLECTION{2001Bossavit, AUTHOR = {Alain Bossavit}, TITLE = {`{G}eneralized finite differences' in computational electromagnetics}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {45--64}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @TECHREPORT{2001BuffaHiptmairVonpetersdorffSchwab, AUTHOR = {A. Buffa and R. Hiptmair and T. von Petersdorff and C. Schwab}, TITLE = {Boundary Element Methods for Maxwell Equations in Lipschitz Domains}, INSTITUTION = {Department of Mathematics, ETH}, YEAR = {2001}, NUMBER = {2001--05}, ADDRESS = {Zurich, Switzerland}, MONTHY = {July}, } @INCOLLECTION{2001Buksas, AUTHOR = {M. W. Buksas}, TITLE = {Implementing the Perfectly Matched Layer Absorbing Boundary Condition with Mimetic Differencing Schemes}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {383--411}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @ARTICLE{2001CastilloHymanShashkovSteinberg, AUTHOR = {Jos\'{e} Castillo and James M. Hyman and Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {Fourth- and sixth-order conservative finite difference approximations of the divergence and gradient}, JOURNAL = {Appl. Numer. Math.}, FJOURNAL = {Applied Numerical Mathematics. An IMACS Journal}, VOLUME = {37}, YEAR = {2001}, NUMBER = {1-2}, PAGES = {171--187}, ISSN = {0168-9274}, CODEN = {ANMAEL}, MRCLASS = {65D25}, MRNUMBER = {2002f:65030}, MRREVIEWER = {Mu Sheng Wei}, } @INCOLLECTION{2001ClemensWeiland, AUTHOR = {Markus Clemens and Thomas Weiland}, TITLE = {Discrete electromagnetism with the {F}inite {I}ntegration {T}echnique}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {65--87}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @INCOLLECTION{2001GrossKotiuga, AUTHOR = {P. W. Gross and P. R. Kotiuga}, TITLE = {{Data structures for geometric and topological aspects of finite element algorithms}}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {151--169}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @INCOLLECTION{2001GrossKotiugaB, AUTHOR = {P.W. Gross and P. R. Kotiuga}, TITLE = {Finite Element-Based Algorithms to Make Cuts for Magnetic Scalar Potentials: Topological Constraints and Computational Complexity}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {207--245}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @ARTICLE{2001Hiptmair, AUTHOR = {R. Hiptmair}, TITLE = {High order {W}hitney forms}, JOURNAL = {J. Electr. Waves and Appl.}, VOLUME = {15}, NUMBER = {3}, YEAR = {2001}, PAGES = {291--436}, } @ARTICLE{2001HiptmairB, AUTHOR = {R. Hiptmair}, TITLE = {Discrete {H}odge operators}, JOURNAL = {Numer. Math.}, FJOURNAL = {Numerische Mathematik}, VOLUME = {90}, YEAR = {2001}, NUMBER = {2}, PAGES = {265--289}, ISSN = {0029-599X}, CODEN = {NUMMA7}, MRCLASS = {39A05 (35J25 35K57 39A12 65N06)}, MRNUMBER = {1 872 728}, MRREVIEWER = {Thomas H. Sonar}, } @INCOLLECTION{2001HiptmairC, AUTHOR = {R. Hiptmair}, TITLE = {{Higher order {W}hitney forms}}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {271--299}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @INCOLLECTION{2001HiptmairD, AUTHOR = {R. Hiptmair}, TITLE = {Discrete {H}odge-Operators: An Algebraic Perspective}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {247--269}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @UNPUBLISHED{2001HymanCampbellShashkov, AUTHOR = {James M. Hyman and J. Campbell and Mikhail J. Shashkov}, TITLE = {Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids}, NOTE = {LA-UR-01-1806, Submitted to Computers \& Mathematics with Applications}, } @UNPUBLISHED{2001HymanMorelShashkovSteinberg, AUTHOR = {James M. Hyman and J. Morel and Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {Mimetic Finite Difference Methods for Diffusion Equations}, NOTE = {LA-UR-01-2434, Submitted to Journal of Computational Geosciences.{\em NOTES: }Recommended.} } @INCOLLECTION{2001HymanShashkov, AUTHOR = {James M. Hyman and Mikhail J. Shashkov}, TITLE = {Mimetic Finite Difference Methods for {M}axwell's Equations and the Equations of Magnetic Diffusion}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {89--121}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @ARTICLE{2001HymanShashkovSteinberg, AUTHOR = {James M. Hyman and Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {The effect of inner products for discrete vector fields on the accuracy of mimetic finite difference methods}, JOURNAL = {Comput. Math. Appl.}, FJOURNAL = {Computers \& Mathematics with Applications. An International Journal}, VOLUME = {42}, YEAR = {2001}, NUMBER = {12}, PAGES = {1527--1547}, ISSN = {0898-1221}, CODEN = {CMAPDK}, MRCLASS = {65N06}, MRNUMBER = {2002k:65172}, MRREVIEWER = {John C. Strikwerda}, } @InProceedings{2001KarasozenTsybulin, author = {B\"ulent Karas\"ozen and Vyacheslav G. Tsybulin}, title = {Conservative finite difference schemes for cosymmetric systems}, booktitle = {CASC 2001. Proceedings of the 4th international workshop, Konstanz, Germany, September 22-26, 2001. Berlin}, pages = {363--375}, year = {2001}, editor = {Victor G. Ganzha,}, publisher = {Springer}, } @Unpublished{2001KitsonMclachlanRobidoux, author = {A. Kitson and R. I. McLachlan and N. Robidoux}, title = {Skew-adjoint finite difference methods}, note = {Accepted for publication in the {\em New Zealand Journal of Mathematics.}}, year = {2001}, } @Article{2001KoleFiggeDeRaedt, author = {J. S. Kole and M. T. Figge and H. De Raedt}, title = {Unconditionally Stable Algorithms to Solve the Time-Dependent Maxwell Equations}, journal = {Physical Review E}, volume = {64}, month = {December}, number = {6}, pages = {1--14}, year = {2001}, } @TECHREPORT{2001LiskaGanzhaZenger, AUTHOR = {R. Liska and V. Ganzha and C. Zenger}, TITLE = {Mimetic Finite Difference Methods for Elliptic Equations on Unstructured Grids}, YEAR = {2001}, INSTITUTION = {Los Alamos National Laboratory}, NUMBER = {LA-UR-01-6955}, ADDRESS = {Los Alamos, NM}, NOTE = {Also TUM-I0108. http://cnls.lanl.gov/$\sim$shashkov/ }, URL = {http://cnls.lanl.gov/~shashkov/}, } @INCOLLECTION{2001Marrone, AUTHOR = {M. Marrone}, TITLE = {Computational Aspects of the Cell Method in Electrodynamics}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {317--356}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @INCOLLECTION{2001Mattiussi, AUTHOR = {C. Mattiussi}, TITLE = {{The geometry of time-stepping}}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {123--149}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @UNPUBLISHED{2001MeyerDesbrunSchroederBarr, AUTHOR = {Mark Meyer and Mathieu Desbrun and Peter Schroeder and Alan H. Barr}, TITLE = {Discrete Differential-Geometry Operators for Triangulated 2-Manifolds}, NOTE = {Preprint: See {\tt http://www-grail.usc.edu/pubs.html}}, URL = {http://www-grail.usc.edu/pubs.html}, } @ARTICLE{2001MorelHallShashkov, AUTHOR = {J. Morel and M. Hall and Mikhail J. Shashkov}, TITLE = {A local support-operators diffusion discretization scheme for hexahedral meshes}, JOURNAL = {J. Comput. Phys.}, FJOURNAL = {Journal of Computational Physics}, VOLUME = {170}, YEAR = {2001}, NUMBER = {1}, PAGES = {338--372}, ISSN = {0021-9991}, CODEN = {JCTPAH}, MRCLASS = {65N06}, MRNUMBER = {2002e:65156}, MRREVIEWER = {John C. Strikwerda}, URL = {http://cnls.lanl.gov/~shashkov}, } @INCOLLECTION{2001Puska, AUTHOR = {P. Puska}, TITLE = {Covariant Isotropic Constitutive Relations in Clifford's Geometric Algebra}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {413--428}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @BOOK{2001Samarskii, AUTHOR = {Alexander A. Samarskii}, TITLE = {The theory of difference schemes}, SERIES = {Monographs and Textbooks in Pure and Applied Mathematics}, VOLUME = {240}, PUBLISHER = {Marcel Dekker Inc.}, ADDRESS = {New York}, YEAR = {2001}, PAGES = {xviii+761}, ISBN = {0-8247-0468-1}, MRCLASS = {65-02 (65M06 65M12 65N06 65N12)}, MRNUMBER = {2002c:65003}, MRREVIEWER = {Raytcho Lazarov}, NOTE = {Translated from the Russian.}, } @UNPUBLISHED{2001Seiler, AUTHOR = {Werner M. Seiler}, TITLE = {Completion to Involution and Semi-Discretization}, NOTE = {Preprint: See {\tt http://www.math.uni-mannheim.de/\~{}wms} }, URL = {http://www.math.uni-mannheim.de/~wms}, } @INCOLLECTION{2001TarhasaariKettunen, AUTHOR = {T. Tarhasaari and L. Kettunen}, TITLE = {{Topological approach to computational electromagnetism}}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {189--206}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @BOOK{2001Teixeira, EDITOR = {F. L. Teixeira}, TITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, YEAR = 2001, } @INCOLLECTION{2001TeixeiraB, AUTHOR = {F. L. Teixeira}, TITLE = {{Geometrical aspects of the simplicial discretization of {M}axwell's equations}}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {171--188}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @INCOLLECTION{2001Tonti, AUTHOR = {Enzo Tonti}, TITLE = {{Finite formulation of the electromagnetic field}}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {1--44}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @INCOLLECTION{2001Vanrienen, AUTHOR = {U. van Rienen}, TITLE = {Frequency Domain Analysis of Waveguides and Resonators with FIT on Non-orthogonal Triangular Grids}, BOOKTITLE = {Geometric Methods in Computational Electromagnetics, {P}{I}{E}{R} 32}, EDITOR = {F. L. Teixeira}, PUBLISHER = {EMW Publishing}, ADDRESS = {Cambridge, Mass.}, PAGES = {357--381}, YEAR = 2001, CROSSREF = {2001Teixeira}, } @INPROCEEDINGS{2002Arnold, AUTHOR = {Douglas N. Arnold}, TITLE = {Differential complexes and numerical stability}, BOOKTITLE = {Proceedings of the International Congress of Mathematicians, Beijing 2002}, YEAR = {2002}, NOTE = {The transparencies from the ICM address are found at http://www.ima.umn.edu/~arnold/talks/icm2002.pdf}, URL = {http://ima.umn.edu/~arnold/papers/icm2002.pdf or http://www.ima.umn.edu/preprints/aug2002/1875.pdf}, } @ARTICLE{2002DeHoopLagerJorna, AUTHOR = {Adrianus T. de Hoop and Ioan E. Lager and Pieter Jorna}, TITLE = {The Space-Time Integrated Model of Electromagnetic Field Computation}, JOURNAL = {Electromagnetics}, YEAR = {2002}, NUMBER = {22}, PAGES = {371--379} } @BOOK{2002EstepTavener, EDITOR = {Donald Estep and Simon Tavener}, TITLE = {Collected Lectures on the Preservation of Stability Under discretization}, PUBLISHER = {SIAM}, ADDRESS = {Philadelphia}, YEAR = {2002}, } @ARTICLE{2002Hiptmair, AUTHOR = {R. Hiptmair}, TITLE = {Finite elements in computational electromagnetism}, JOURNAL = {Acta Numerica}, YEAR = {2002}, PAGES = {237--339}, VOLUME = {11}, MONTH = {January}, } @INCOLLECTION{2002HymanMorelShashkovSteinberg, AUTHOR = {James M. Hyman and J. Morel and Mikhail J. Shashkov and Stanly Steinberg}, TITLE = {Mimetic Finite Difference Methods for Diffusion Equations}, BOOKTITLE = {Locally Conservative Numerical Methods for Flow in Porous Media}, EDITOR = {M. G. Edwards and R. Lazarov and I. Yotov}, JOURNAL = {Journal of Computational Geosciences}, VOLUME = {6}, YEAR = {2002}, PAGES = {333--353}, } @UNPUBLISHED{2002HymanSteinberg, AUTHOR = {James M. Hyman and Stanly Steinberg}, TITLE = {Convergence of Mimetic Discretization for Rough Grids}, NOTE = {Submitted for publication}, } @ARTICLE{2002Mattiussi, AUTHOR = {Claudio Mattiussi}, TITLE = {A reference discretization strategy for the numerical solution of physical field problems}, JOURNAL = {Advances in Imaging and Electron Physics}, VOLUME = {121}, YEAR = {2002}, PAGES = {143--279}, } @PHDTHESIS{2002Robidoux, AUTHOR = {Nicolas Robidoux}, TITLE = {Numerical Solution of the Steady Diffusion Equation with Discontinuous Coefficients}, SCHOOL = {University of New Mexico}, ADDRESS = {Albuquerque, NM}, YEAR = {2002}, MONTH = {May}, PAGES = {xxiv+131}, URL = {http://citeseer.nj.nec.com/robidoux02numerical.html or http://www.math.sfu.ca/~nrobidou/public_html/prints/thesis/thesis.pdf}, } @UNPUBLISHED{2002RobidouxSteinberg, AUTHOR = {Nicolas Robidoux and Stanly Steinberg}, TITLE = {A Discrete Vector Calculus in Tensor Grids}, YEAR = {2002}, URL = {http://math.unm.edu/~stanly/}, } @UNPUBLISHED{2002Steinberg, AUTHOR = {Stanly Steinberg}, TITLE = {A Discrete Calculus with Applications to Discretizing Boundary-Value Problems}, YEAR = {2002}, NOTE = {Preprint.}, URL = {http://math.unm.edu/~stanly/}, }