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UPML formulation for truncating conductive media in curvilinear coordinates

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Abstract

This work presents a formulation based on UPML for truncating conductive media by using a local and non-orthogonal coordinate system to solve Maxwell’s equations by the FDTD method. The detailed procedure for obtaining the UPML equations for this case is shown and the complete equation set is provided.

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References

  1. Bayliss, A., Turkel, E.: Radiation boundary conditions for wave-like equations. Comm. Pure Appl. Math. 23, 707–725 (1980)

    Article  MathSciNet  Google Scholar 

  2. Berenger, J.: A perfectly matched layer for the absorption of electromagnetic waves. J. Computational Phisics 114, 185–200 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gedney, S.D.: An anisotropic perfectly matched layer absorbing media for the truncation of FDTD latices. IEEE Trans. Antennas Propag. 44, 1630–1639 (1996)

    Article  Google Scholar 

  4. Gedney, S.D., Roden, J.A.: Numerical stability of nonorthogonalFDTD methods. IEEE Trans. Antennas Propag. 48(2), 231–239 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Higdon, R.: Numerical absorbing boundary conditions for the wave equation. Math. Comput. 49, 65–90 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  6. Holland, R., Williams, J.: Total-field versus scattered-field finite-difference. IEEE Trans. Nucl. Sci. 30, 4583–4588 (1983)

    Article  Google Scholar 

  7. Liao, Z., Wong, H., Yang, B.P., Yuan, Y.F.: A transmitting boundary for transient wave analysis. Sci. Sin. XXVII(series A), 1063–1076 (1984)

    Google Scholar 

  8. Mur, G.: Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations. IEEE Trans. Electromagn. Compat. 23, 377–382 (1981)

    Article  Google Scholar 

  9. Taflove, A., Hagness, S.C.: Computational Electrodynamics, The Finite-Difference Time-Domain Method. Artech House Inc., 3 edn. (2005)

  10. Tuma, E.T., de Oliveira, R.M.S., Sobrinho, C.L.S.S.: New model of current impulse injection and potential measurement in transient analysis of grounding systems in homogeneous and stratified soils using the FDTD method. In: International Symposium on Lightning Protection (SIPDA). Sao Paulo, Brazil (2005)

  11. Yee, K.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14, 302–307 (1966)

    Article  MATH  Google Scholar 

  12. Yung, E.K.-N., Tam, W.-Y.: Analysis of a circular earthing plate. In: IEE proceedings. Part C. Generation, transmission and distribution (IEE Proc. C) (1989)

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Correspondence to Rodrigo M. S. de Oliveira.

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de Oliveira, R.M.S., Sobrinho, C.L.S.S. UPML formulation for truncating conductive media in curvilinear coordinates. Numer Algor 46, 295–319 (2007). https://doi.org/10.1007/s11075-007-9139-6

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  • DOI: https://doi.org/10.1007/s11075-007-9139-6

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