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Finite Elements in Electromagnetics 4. Wave problems

Finite Elements in Electromagnetics 4. Wave problems. Oszkár Bíró IGTE, TU Graz Kopernikusgasse 24Graz, Austria email: biro@igte.tu-graz.ac.at. Overview. Maxwell‘s equations Resonators Filters Wave propagation in free space. Maxwell‘s equations. Time harmonic case. Resonators. G E :.

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Finite Elements in Electromagnetics 4. Wave problems

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  1. Finite Elements in Electromagnetics4. Wave problems Oszkár Bíró IGTE, TU Graz Kopernikusgasse 24Graz, Austria email: biro@igte.tu-graz.ac.at

  2. Overview • Maxwell‘s equations • Resonators • Filters • Wave propagation in free space

  3. Maxwell‘s equations Time harmonic case

  4. Resonators GE: GH:

  5. Resonators, H-formulation A problem without excitation: Eigenvalue problem

  6. Resonators, operator equation for H

  7. Resonators, finite element Galerkin equations for H i = 1, 2, ..., n Generalized algebraic eigenvalue problem

  8. Filters GH: GE: GH:

  9. Filters, E-formulation A problem with excitation: Driven problem

  10. Filters, operator equation for E

  11. Filters, finite element Galerkin equations for E i = 1, 2, ..., n conditioning of [A] strongly depends on frequency

  12. Filters, A,V-formulation

  13. Filters, operator equation for A,V

  14. Filters, finite element Galerkin equations for A,V (1)

  15. Filters, finite element Galerkin equations for A,V (2) i = 1, 2, ..., n(e) i = 1, 2, ..., n(n)

  16. Filters, finite element Galerkin equations for A,V (3) [A] is singular and its conditioning depends less on frequency R. Dyczij-Edlinger and O. Biro, "A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements," IEEE Transactions on Microwave Theory and Techniques, vol. 44, pp. 15-23, January 1996.

  17. Wave propagation in free space • Finite element method needs closed domain • Modeling of infinite space necessary • Perfectly matched layers (PMLs) PML

  18. y PML x z PMLs Nonphysical material properties No reflection on the interface between air and PML

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