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An \(hp\)-adaptive finite element method for electromagnetics. I: Data structure and constrained approximation. (English) Zbl 0979.78031
Summary: This is the first of several papers describing an implementation of the \(hp\)-adaptive, mixed finite element (FE) method for the solution of steady-state Maxwell’s equations proposed in L. Demkowicz and L. Vardapetyan [Comput. Methods Appl. Mech. Eng. 152, 103-124 (1998; Zbl 0994.78011)]. The discretization is defined on a hybrid grid consisting of both triangles and quads and allows for both \(h\)- and \(p\)-refinements of the mesh. The paper focuses on the data structure and constrained approximation issues and provides a number of illustrative examples.

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
35Q60 PDEs in connection with optics and electromagnetic theory
HP90; 2Dhp90
Full Text: DOI
[1] M. Cessenat, Mathematical methods in electromagnetism, Linear theory and applications, World Scientific, London, 1996 · Zbl 0917.65099
[2] L. Demkowicz, A posteriori error analysis for steady-state Maxwell’s equations, in: P. Ladaveze, J.T. Oden (Eds.), On New Advances in Adaptive Computational Methods in Mechanics, Elsevier (in print)
[3] L. Demkowicz, K. Gerdes, C. Schwab, A. Bajer, T. Walsh, HP90: A General and Flexible Fortran 90 hp-FE Code, Seminar für Angewandte Mathematik Report 97-17, ETH Zürich, CH-8092 Zürich, December, 1997 · Zbl 0912.68014
[4] L. Demkowicz, P. Monk, Ch. Schwab, L.Vardapetyan, Maxwell eigenvalues and discrete compactness, TICAM Report (in preparation) · Zbl 0998.78011
[5] Demkowicz, L.; Oden, L.J.T.; Rachowicz, W., Toward a universal hp-adaptive finite element strategy part 1, Constrained approximation and data structure, computer methods in applied mechanics and engineering, 77, 79-112, (1989) · Zbl 0723.73074
[6] L. Demkowicz, M. Pal, An infinite element for Maxwell’s equations, Computers Methods in Applied Mechanics and Engineering 164 (1998) 77-94 · Zbl 1034.78018
[7] Demkowicz, L.; Vardapetyan, L., Modeling of electromagnetic absoption/scattering problems using hp-adaptive finite elements, Computer methods in applied mechanics and engineering, 152, 103-124, (1998) · Zbl 0994.78011
[8] L. Demkowicz, T. Walsh, K. Gerdes, A. Bajer, 2D hp-adaptive finite element package, Fortran 90 Implementation (2Dhp90), TICAM Report 98-14, The University of Texas at Austin, Austin, TX 78712 · Zbl 0912.68014
[9] Fikioris, J.G.; Tsalamengas, J.L.; Fikioris, G.J., Exact solutions for shielded printed microstrip lines by the Carleman-Vekua method, IEEE transcations on microwave theory and techniques, 37, 1, (1989)
[10] J. Jin, The Finite Element Method in Electromagnetics, Wiley, New York 1993 · Zbl 0823.65124
[11] L.P. Meissner, Fortran 90, PWS Publishing Company, Boston 1995
[12] Nedelec, J.C., Mixed finite elements in IR, Numerische Mathematik, 35, 315-341, (1980) · Zbl 0419.65069
[13] Nedelec, J.C., A new family of mixed finite elements in R3, Numerische Mathematik, 50, 57-81, (1986) · Zbl 0625.65107
[14] C.R. Paul, S.A. Nasar, Introduction to electromagnetic fields, McGraw-Hill, New York, 1987
[15] L. Vardapetyan, L. Demkowicz, hp-adaptive finite elements in electromagnetics, Computers Methods in Applied Mechanics and Engineering 169 (1999) 331-344 · Zbl 0956.78013
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