A comparative Analysis of Cylindrical CFS-PML ABC for Finite Volume Simulations in the Frequency Domain

Ana Paula M. Lima, Marcela S. Novo

Abstract


A comparative analysis of two cylindrical complex-frequency-shifted perfectly matched layers (CFS-PML) absorbing boundary condition (ABC) for bi-dimensional (2-D) finite-volume (FV) simulations in the frequency domain is presented. The impact of CFS-PML parameters on the wave absorption, as well as on the condition number of the associated system matrix is investigated by comparing the performance of two PML loss profiles, viz., polynomial and geometric grading. FV-CFS-PML results are validated against analytical solution. Numerical results show that inclusion of a CFS-PML within the FV computational domain increases the condition number of the system matrix and therefore the use of CFS-PML 3-D FV simulations is limited.

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References


A. Taflove and S. Hagness, Computational Eletrodynamics: The Finite-Difference Time-Domain Method, Boston MS: Artech House, 2005.

U. Pekel and R. Mittra, A finite element method frequency-domain application of the perfectly matched layer (PML) concept, Microwave Opt. Technol. Lett., vol. 9, pp.117 -122, 1995.

Y. Y. Botros and J. L. Volakis, Preconditioned generalized minimal residual iterative scheme for perfectly matched layer terminated applications, IEEE Micro. and Guide Wave Lett., vol. 9, no.2, Feb. 1999.

D. Pardo, L. Demkowicz, C. Torres-Verdin, and C. Michler, PML Enhanced With A Self-Adaptive Goal-Oriented pp- Finite Element Method: Simulation Of Through-Casing Borehole Resistivity Measurements, Siam Journal on Scientific Computing, vol 30, no. 6, pp. 2948-2964, 2008.

H. O. Lee, F. L. Teixeira, L. E. San Martin, and M. S. Bittar, Numerical modeling of eccentered LWD borehole sensors in dipping and fully anisotropic Earth formations, IEEE Trans. Geosci. Remote Sens., vol. 50, no. 3, pp. 727-735, 2012.

J. M. Jin and W.C. Chew, Combining PML and ABC for Finite Element Analysis of Scattering Problems, Micro. and Opt. Tech. Lett., vol. 12, no. 4, pp. 192-197, Jul. 1996.

Y. Y. Botros and J. L. Volakis, Perfectly Matched Layer Termination for Finite-Element Meshes: Implementation and Application, Micro. and Opt. Tech. Lett., vol. 23, no. 7, pp. 166-172, Nov. 1999.

B. Stupfel, A Study of the Condition Number of Various Finite Element Matrices Involved in the Numerical Solution of Maxwell's Equations, IEEE Trans. Antennas Propagat., vol. 52, no. 11, pp. 3048-3059, Nov. 2004.

E. S. Um, J. M. H. and D. L. Alumbaugh, An iterative finite-element time-domain method for simulating three-dimensional electromagnetic diffusion in earth, Geophysical Journal International, vol.190, no.2, pp. 871-886, Aug. 2012.

Y.K. Hue and F. L. Teixeira, Numerical Mode-Matching Method for Tilted-Coil Antennas in Cylindrically Layered Anisotropic Media With Multiple Horizontal Beds, IEEE Trans. Geoscience Remote Sens., vol.45, no.8, pp.2451-2462, 2007.

M. S. Novo, L. C. da Silva and F. L. Teixeira, Finite Volume Modeling of Borehole Electromagnetic Logging in 3-D Anisotropic Formations Using Coupled Scalar-Vector potentials, IEEE Antennas Wireless Propag. Lett., vol. 6, pp. 549-552, 2007.

M. S. Novo, L. C. da Silva and F. L. Teixeira, Comparison of Coupledpotentials and Field-Based Finite-Volume Techniques for Modeling of Borehole EM Tools, IEEE Geosci. Remote Sens. Lett., vol. 5, pp. 209-211, 2008.

M. S. Novo, L. C. da Silva and F. L. Teixeira, Three-Dimensional Finite-Volume Analysis of Directional Resistivity Logging Tools, IEEE Trans. Geosci. Remote Sens., vol. 48, pp. 1151-1158, Mar. 2010.

M. S. Novo, L. C. da Silva and F. L. Teixeira, A Comparative Analysis of Krylov Solvers for Three-Dimensional Simulations of Borehole Sensors, IEEE Geosci. Remote Sens. Lett., vol. 8, no. 1, pp. 98-102, Jan. 2011.

L. F. Ribeiro and M. S. Novo, Analysis of the Cylindrical PML ABC for 2-D Finite Volume Simulations in the Frequency Domain, Proceedings of 2011 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, 2011, Natal.

A. P. M. Lima and M. S. Novo, Analysis of Cylindrical CFS-PML ABC for 2-D Finite Volume Simulations in the Frequency Domain, Proceedings of of 2013 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, 2013, Rio de Janeiro.

M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched absorbers,†IEEE Microwave Guided Wave Lett., vol. 6, pp. 447–449, Dec. 1996.

M. S. Novo, Análise numérica de sensores eletromagnéticos de prospecção petrolífera utilizando o método dos volumes finitos, Pontifícia Universidade Católica do Rio de Janeiro, Departamento de Engenharia Elétrica, Tese de Doutorado, Agosto 2007.

F. L. Teixeira and W. C. Chew, Sistematic Derivation of Anisotropic PML Absorbing Media in Cylindrical and Spherical Coordinates, IEEE Microwave Guided Wave Lett., vol. 7, no. 11, pp. 371-373, Nov. 1997.




DOI: http://dx.doi.org/10.1590/2179-10742014v13i2394

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