A discrete differential forms framework for computational electromagnetism

CMES - Computer Modeling in Engineering and Sciences

Volumn 5, Issue 4, 2004, Pages 331-345

  Castillo, P ^a   Koning, J ^b   Rieben, R ^c   White, D ^b  

^a UNIVERSITY OF PUERTO RICO   (Puerto Rico)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Computational electromagnetism; H(div) and H(curl) conforming methods; High order finite element; Object oriented programming

Indexed keywords

COMPUTATIONAL ELECTROMAGNETISM; HIGH ORDER FINITE ELEMENT; RADIATION TRANSPORT;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; ELECTRIC FIELDS; ELECTRIC POTENTIAL; FINITE ELEMENT METHOD; MAGNETIC FIELDS; MAGNETIC FLUX; OBJECT ORIENTED PROGRAMMING; PROBLEM SOLVING;

ELECTROMAGNETISM;

EID: 5144223937     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. Abraham, R.; Marsden, J. E.; Ratiu, T. (1996): Manifolds, Tensor Analysis, and Applications. Applied Mathematical Sciences.
2. Babaska, I.; Ihlenburg, F.; Strouboulis, T.; Gangaraj, S. K. (1997): A posteriori error estimation for finite element solution of Helmholtz. Internat. J. Numer. Methods Engrg., vol. 40, no. 21, pp. 3883-3900.
3. Babuska, I.; Strouboulis, T.; Upadhyay, C.; 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 Engrg., vol. 38, no. 24, pp. 4207-4235.
4. Baldomir, D. (1986): Differential forms and electromagnetism in 3-dimensional Euclidean space R3. IEEE Proceedings., vol. 133, no. 3, pp. 139-143.
5. Bossavit, A. (1998): Computational Electromagnetism: variational formulation, complementarity, edge elements. Academic Press.
6. Burke, W. (1985): Applied Differential Geometry: variational formulation. Cambridge University Press.
7. Ciarlet, P. G. (1978): The Finite Element Method for Elliptic Problems. North-Holland.
8. Deschamps, G. (1981): Electromagnetics and differential forms. IEEE Proceedings., vol. 69, no. 6, pp. 676-687.
9. Graglia, R.; Wilton, P.; Peterson, A. (1997): Higher order interpolatory vector bases for computational electromagnetics. IEEE Trans. Ant. Prop., vol. 45, no. 3, pp. 329-342.
10. Graglia, R.; Wilton, P.; Peterson, A.; Gheorma, I.L. (1998): Higher order interpolatory vector bases on prism elements. IEEE Trans. Ant. Prop., vol. 46, no. 3, pp. 442-450.
11. Hesthaven, J. S.; Warburton, T. (2004): High-order accurate methods for time-domain electromagnetics. CMES: Computer Modeling in Engineering & Sciences, vol. 5, no. 5, pp. 395-408.
12. Hiptmair, R. (1998): Multigrid method for 'Maxwell's equations. SIAM J. Num. Anal., vol. 38, no. 1, pp. 204-225.
13. Hiptmair, R. (1999): Canonical construction of finite elements. Math. Comp., vol. 68, no. 228, pp. 1325-1346.
14. Hiptmair, R. (2001): Discrete Hodge operators: An algebraic perspective. J. Electromagnteic Waves Appl., vol. 15, no. 3, pp. 343-344.
15. Jin, J. (1993): The Finite Element Method in Electromagnetics. Wiley.
16. Nambura, R. R.; Mark, E. R.; Clarke, J. A. (2004): Scalable electromagnetic simulation environment. CMES: Computer Modeling in Engineering & Sciences, vol. 5, no. 5, pp. 443-454.
17. Nédélec, J. C. (1980): Mixed Finite Elements in r3. Numer. Math., vol. 35, pp. 315-341.
18. Nédélec, J. C. (1986): A New Family of Mixed Finite Elements in r3. Numer. Math., vol. 50, pp. 57-81.
19. Rachowicz, W.; Demkowicz, L. (2002): An hpadaptive finite element method for electromagnetics. vol. 53, no. 1, pp. 147-180.
20. nd Order Elliptic Problems. In Galligani, I.; Mayera, E.(Eds): Mathematical Aspects of the Finite Element Method, volume 606 of Lect. Notes. on Mathematics, pp. 293-315. Springer Verlag.
21. Rieben, R.; White, D.; Rodrigue, G. (2004): High order symplectic integration methods for finite element solutions to time dependent maxwell equations. IEEE Trans. Ant. Prop. in press.
22. Rieben, R.; White, D.; Rodrigue, G. (2004): Improved conditioning of finite element matrices using new high order interpolatory bases. IEEE Trans. Ant. Prop. in press.
23. Rodrigue, G.; White, D. (2001): A vector finite element time-domain method for solving Maxwell's equations on unstructured hexahedral grids. SIAM J. Sci. Comp., vol. 23, no. 3, pp. 683-706.
24. Schinnerl, S.; Schoberl, M.; Kaltenbacher, M. (2000): Nested multigrid methods for the fast numerical computation of 3d fields. IEEE Trans. Mag., vol. 36, no. 4, pp. 1557-1560.
25. Stroustrup, B. (1991): C++ Programming Language. Addison-Wesley, Reading, MA.
26. Warren, S.; Scott, W. (1994): An investigation of numerical dispersion in the vector finite element method using quadrilateral elements. IEEE Trans. Ant. Prop., vol. 42, no. 11, pp. 1502-1508.
27. Warren, S.; Scott, W. (1995): Numerical dispersion in the finite element method using triangular edge elements. Opt. Tech. Lett., vol. 9, no. 6, pp. 315-319.
28. White, D. (2000): Numerical dispersion of a vector finite element method on skewed hexahedral grids. Commun. Numer. Meth. Engng., vol. 16, pp. 47-55.
29. White, D.; Koning, J. (2002): A novel approach for computing solenoidal eigenmodes of the vector Helmholtz equation. IEEE Trans. Mag., vol. 38, no. 5, pp. 3420-3425.