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FEMSTER: An object-oriented class library of high-order discrete differential forms

Authors:

Daniel WhiteAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 31, Issue 4

Pages 425 - 457

https://doi.org/10.1145/1114268.1114269

Published: 01 December 2005 Publication History

Abstract

FEMSTER is a modular finite element class library for solving three-dimensional problems arising in electromagnetism. The library was designed using a modern geometrical approach based on differential forms (or p-forms) and can be used for high-order spatial discretizations of well-known H(div)- and H(curl)-conforming finite element methods. The software consists of a set of abstract interfaces and concrete classes, providing a framework in which the user is able to add new schemes by reusing the existing classes or by incorporating new user-defined data types.

References

[1]

Abraham, R., Marsden, J. E., and Ratiu, T. 1996. Manifolds, Tensor Analysis, and Applications, 2nd ed. Springer series in Applied Mathematical Sciences. Springer Verlag, Berlin, Germany.

[2]

Ainsworth, M. 2004. Discrete dispersion relation for hp-version finite element approximation at high wave number. SIAM J. Num. Anal. 42, 2, 553--575.

[3]

Ainsworth, M. and Coyle, J. 2001a. Conditioning of hierarchic p-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra. Tech. rep., Department of Mathematics, University of Strathclyde, Glasgow, U.K.

[4]

Ainsworth, M. and Coyle, J. 2001b. Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes. Comput. Methods Appl. Mech. Eng. 190, 6709--6733.

[5]

Ainsworth, M. and Coyle, J. 2002. Hierarchic finite element bases on unstructured tetrahedral meshes. Tech. rep., Department of Mathematics, University of Strathclyde, Glasgow, U.K.

[6]

Ainsworth, M. and Coyle, J. 2003. Computation of Maxwell eingenvalues on curvilinear domains using hp-version of Nédélec elements. Tech. rep., Department of Mathematics, University of Strathclyde, Glasgow, U.K.

[7]

Babuska, I., Ihlenburg, F., Strouboulis, T., and Gangaraj, S. K. 1997. A posteriori error estimation for finite element solution of Helmholtz. Internat. J. Numer. Methods Eng. 40, 21, 3883--3900.

[8]

Babuska, I., Strouboulis, T., Upadhyay, C., and Gangaraj, S. K. 1995. A posteriori estimation and adaptive control of the pollution error in the h-version of the finite element method for finite element solution of Helmholtz. Internat. J. Numer. Methods Eng. 38, 24, 4207--4235.

[9]

Baldomir, D. 1986. Differential forms and electromagnetism in 3-dimensional Euclidean space R3. IEEE Proc. 133, 3, 139--143.

[10]

Bossavit, A. 1998. Computational Electromagnetism: Variational Formulation, Complementarity, Edge Elements. Academic Press (currently part of Elsevier, Burlington, MA).

[11]

Brezzi, F. and Fortin, M. 1991. Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics. Springer Verlag, Berlin, Germany.

[12]

Burke, W. 1985. Applied Differential Geometry: Variational Formulation. Cambridge University Press, Cambridge, U.K.

[13]

Ciarlet, P. G. 1978. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, The Netherlands.

[14]

Clemens, M. and Weiland, T. 2001. Discrete electromagnetism with the finite integration technique. In Geometric Methods for Computational Electromagnetics, F. Texeira, ed. Vol. 32 of PIER. EMW Publishing, Cambridge, MA, 189--206.

[15]

Deschamps, G. 1981. Electromagnetics and differential forms. IEEE Proc. 69, 6, 676--687.

[16]

Graglia, R., Wilton, P., and Peterson, A. 1997. Higher order interpolatory vector bases for computational electromagnetics. IEEE Trans. Ant. Prop. 45, 3, 329--342.

[17]

Graglia, R., Wilton, P., Peterson, A., and Gheorma, I.-L. 1998. Higher order interpolatory vector bases on prism elements. IEEE Trans. Ant. Prop. 46, 3, 442--450.

[18]

Hiptmair, R. 1999. Canonical construction of finite elements. Math. Comp. 68, 228, 1325--1346.

[19]

Hiptmair, R. 2001. Discrete Hodge operators: An algebraic perspective. J. Electromag. Waves Appl. 15, 3, 343--344.

[20]

Hiptmair, R. 2002. Finite elements in computational electromagnetism. Acta Numerica, 11, Jan., 237--339.

[21]

Hyman, J. and Shashkov, M. 1999. Mimetic discretization for Maxwell's equations. J. Comput. Phys. 151, 2, 881--909.

[22]

Nédélec, J. C. 1980. mixed finite elements in r3. Numer. Math. 35, 315--341.

[23]

Nédélec, J. C. 1986. A new family of mixed finite elements in r3. Numer. Math. 50, 57--81.

[24]

Raviart, P. and Thomas, J. 1977. A mixed finite element method for 2nd order elliptic problems. In Mathematical Aspects of the Finite Element Method, I. Galligani and E. Mayera, eds. Lecture Notes. in Mathematics, vol. 606. Springer Verlag, Berlin, Germany, 293--315.

[25]

Rieben, R., Rodrigue, G., and White, D. 2005. A high order mixed finite element method for solving the time dependent Maxwell equations on unstructured grids. J. Computat. Phys. 204, 4, 490--579.

[26]

Rodrigue, G. and White, D. 2001. A vector finite element time-domain method for solving Maxwell's equations on unstructured hexahedral grids. SIAM J. Sci. Comp. 23, 3, 683--706.

[27]

Stroustrup, B. 1991. C++ Programming Language. Addison-Wesley, Reading, MA.

[28]

Tarhasaari, T. and Kettunen, L. 2001. Topological approach to computational electromagnetism. In Geometric Methods for Computational Electromagnetics, F. Texeira, ed. Vol. 32 of PIER. EMW Publishing, Cambridge, MA, 189--206.

[29]

Teixeira, F. L. 2001. Geometric Methods in Computational Electromagnetics. Vol. 32 of PIER. EMW Publishing, Cambridge, MA.

[30]

Tonti, E. 2001. A direct formulation of field laws: The cell method. Comput. Mod. Eng. Sci. 2, 2, 237--258.

[31]

Warren, S. and Scott, W. 1994. An investigation of numerical dispersion in the vector finite element method using quadrilateral elements. IEEE Trans. Ant. Prop. 42, 11, 1502--1508.

[32]

Warren, S. and Scott, W. 1995. Numerical dispersion in the finite element method using triangular edge elements. Opt. Tech. Lett. 9, 6, 315--319.

[33]

Weiland, T. 1996. Time domain electromagnetic field computation with finite difference methods. Int. J. Numer. Modelling 9, 295--319.

[34]

White, D. 2000. Numerical dispersion of a vector finite element method on skewed hexahedral grids. Commun. Numer. Meth. Eng. 16, 47--55.

[35]

Whitney, H. 1957. Geometric Integration Theory. Princeton University Press, Princeton, NJ.

[36]

Yee, K. S. 1966. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Ant. Prop. 14, 3, 302--307.

Cited By

Spitzer K(2023)Electromagnetic Modeling Using Adaptive Grids – Error Estimation and Geometry RepresentationSurveys in Geophysics10.1007/s10712-023-09794-945:1(277-314)Online publication date: 22-Jun-2023
https://doi.org/10.1007/s10712-023-09794-9
Mlakar DWinter MStadlbauer PSeidel HSteinberger MZayer R(2020)Subdivision‐Specialized Linear Algebra Kernels for Static and Dynamic Mesh Connectivity on the GPUComputer Graphics Forum10.1111/cgf.1393439:2(335-349)Online publication date: 13-Jul-2020
https://doi.org/10.1111/cgf.13934
Wang FMorten JSpitzer K(2018)Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured gridsGeophysical Journal International10.1093/gji/ggy029213:2(1056-1072)Online publication date: 29-Jan-2018
https://doi.org/10.1093/gji/ggy029
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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 31, Issue 4

December 2005

167 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1114268

Issue’s Table of Contents

Copyright © 2005 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 2005

Published in TOMS Volume 31, Issue 4

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Cited By

Spitzer K(2023)Electromagnetic Modeling Using Adaptive Grids – Error Estimation and Geometry RepresentationSurveys in Geophysics10.1007/s10712-023-09794-945:1(277-314)Online publication date: 22-Jun-2023
https://doi.org/10.1007/s10712-023-09794-9
Mlakar DWinter MStadlbauer PSeidel HSteinberger MZayer R(2020)Subdivision‐Specialized Linear Algebra Kernels for Static and Dynamic Mesh Connectivity on the GPUComputer Graphics Forum10.1111/cgf.1393439:2(335-349)Online publication date: 13-Jul-2020
https://doi.org/10.1111/cgf.13934
Wang FMorten JSpitzer K(2018)Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured gridsGeophysical Journal International10.1093/gji/ggy029213:2(1056-1072)Online publication date: 29-Jan-2018
https://doi.org/10.1093/gji/ggy029
Liu YXu ZLi Y(2018)Adaptive finite element modelling of three-dimensional magnetotelluric fields in general anisotropic mediaJournal of Applied Geophysics10.1016/j.jappgeo.2018.01.012151(113-124)Online publication date: Apr-2018
https://doi.org/10.1016/j.jappgeo.2018.01.012
Zayer RSteinberger MSeidel H(2017)A GPU-Adapted Structure for Unstructured GridsComputer Graphics Forum10.1111/cgf.1314436:2(495-507)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1111/cgf.13144
Na DOmelchenko YMoon HBorges BTeixeira F(2017)Axisymmetric charge-conservative electromagnetic particle simulation algorithm on unstructured grids: Application to microwave vacuum electronic devicesJournal of Computational Physics10.1016/j.jcp.2017.06.016346(295-317)Online publication date: Oct-2017
https://doi.org/10.1016/j.jcp.2017.06.016
Cruz LRamos E(2016)General Template Units for the Finite Volume Method in Box-Shaped DomainsACM Transactions on Mathematical Software10.1145/283517543:1(1-32)Online publication date: 13-Aug-2016
https://dl.acm.org/doi/10.1145/2835175
Jund SSalmon SSonnendrücker E(2015)High-Order Low Dissipation Conforming Finite-Element Discretization of the Maxwell EquationsCommunications in Computational Physics10.4208/cicp.100310.230511a11:3(863-892)Online publication date: 20-Aug-2015
https://doi.org/10.4208/cicp.100310.230511a
Wittke JTezkan B(2014)Meshfree magnetotelluric modellingGeophysical Journal International10.1093/gji/ggu207198:2(1255-1268)Online publication date: 27-Jun-2014
https://doi.org/10.1093/gji/ggu207
Sanchez EPaolini CCastillo J(2014)The Mimetic Methods Toolkit: An object-oriented API for Mimetic Finite DifferencesJournal of Computational and Applied Mathematics10.1016/j.cam.2013.12.046270(308-322)Online publication date: Nov-2014
https://doi.org/10.1016/j.cam.2013.12.046
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