Abstract:
Some EM field problems can be solved in two different, symmetrical ways, which are "complementary" in the sense that each one corrects some deficiencies of the other. In ...Show MoreMetadata
Abstract:
Some EM field problems can be solved in two different, symmetrical ways, which are "complementary" in the sense that each one corrects some deficiencies of the other. In particular, one obtains error bounds this way. Taking as an example the static conduction problem, the authors propose a geometrical presentation of this theory, which generalizes and symmetrizes the classical but a bit forgotten nowadays "hypercircle" principle. The two complementary problems are independent, but they show how having solved one of them allows one to parallelize the solution of the other, by reducing it to a family of local problems (one for each node of the mesh, to be solved in its immediate neighborhood).
Published in: IEEE Transactions on Magnetics ( Volume: 35, Issue: 3, May 1999)
DOI: 10.1109/20.767212
References is not available for this document.
Select All
1.
G. Allen, "Variational Inequalities Complementary Problems and Duality Theory", J. Math. Anal. Appl., vol. 58, pp. 1-10, 1979.
2.
A.M. Arthurs, Complementary variational principles, Oxford:Clarendon Press, 1970.
3.
A. Bossavit, "Complementarity in Non-Linear Magnetostatics: Bilateral Bounds on the Flux-Current Characteristic", COM-PEL, vol. 11, no. 1, pp. 9-12, 1992.
4.
A. Bossavit, Computational Electromagnetism, Boston:Academic Press, 1998.
5.
P. Hammond and J. Penman, "Calculation of inductance and capacitance by means of dual energy principles", Proc. IEE, vol. 123, no. 6, pp. 554-59, 1976.
6.
P. Ladévèze and D. Leguillon, "Error estimate procedure in the finite element method and applications", SIAM J. Numer. Anal., vol. 20, no. 3, pp. 485-509, 1983.
7.
B. Noble, Complementary variational principles for boundary value problems, Nov. 1964.
8.
W. Prager and J.L. Synge, "Approximations in elasticity based on the concept of function space", Quart. Appl. Math., vol. 5, no. 3, pp. 241-69, 1947.
9.
J.N. Reddy and J.T. Oden, "Convergence of Mixed Finite-Element Approximations of a Class of Linear Boundary-Value Problems", J. Struct. Mech., vol. 2, pp. 83-108, 1973.
10.
J.-F. Remacle, P. Dular, A. Genon and W. Legros, "A posteriori error estimation and adaptive meshing using error in constitutive relation", IEEE Trans., vol. MAG-32, no. 3, pp. 1369-72, 1996.
11.
J. Rikabi, C.F. Bryant and E.M. Freeman, "Complementary solutions of linear and non-linear magnetostatic problems", IEE Proc., vol. 135-A, no. 7, pp. 433-47, 1988.
12.
J.L. Synge, The Hypercircle in Mathematical Physics, Cambridge:Cambridge U.P., 1957.
13.
K. Washizu, "Bounds for solutions of boundary value problems in elasticity", J. Math. Phys., pp. 117-28, 1953.
