The research of Peter G. Petropoulos has focused on the numerical modeling and asymptotic analysis of physical problems in the areas of transient electromagnetic wave propagation in complex media. His studies of pulsed electromagnetic waves in dispersive media mainly concern the asymptotic and numerical methods for studying the response of relaxing (Debye) and fractionally-relaxing (Cole-Cole) dielectrics, as well as the development fourth-order accurate finite difference methods for the time-domain Maxwell equations with discontinuous coefficients. His current projects include analysis of the error in problems where impedance boundary conditions are employed, development of numerical techniques to simulate pulse propagation in Cole-Cole dielectrics, analysis of perfectly matched absorbing boundary conditions in relation to exact absorbing boundary conditions, and the development of fourth-order accurate schemes in the presence of curved boundaries.
Scientific Computing, Asymptotic and Perturbation Methods.
Applications in Electromagnetics, Acoustics, and Elasticity.
Absorbing Boundary Conditions
Propagation in Dispersive Media
High-Order Finite Difference Schemes
An Approximate Method for the Study of Transverse Discontinuities in Waveguides, Wave Motion, vol. 13, pp. 123-131, 1991.
Optical Theorems for Electromagnetic Scattering by Inhomogeneities in Layered Dielectric Media, IEEE Transactions on Antennas and Propagation , vol. 39, no. 8, pp. 1119-1124, 1991.
Stability and Phase Error Analysis of FD-TD in Dispersive Dielectrics, IEEE Transactions on Antennas and Propagation, vol. 40, no. 1, pp. 62-69, 1994.
A Simple Guideline for Choosing the Points per Wavelength in FD-TD Simulations, IEEE Antennas and Propagation Magazine, vol. 36, no. 2, pp. 67-68, 1994.
Phase Error Control for FD-TD Methods of Second and Fourth Order Accuracy, IEEE Transactions on Antennas and Propagation, vol. 42, no. 6, pp. 859-862, 1994.
The Wave Hierarchy for Propagation in Relaxing Dielectrics, Wave Motion, vol. 21, pp. 253-262, 1995.
Asymptotic and Energy Estimates for Electromagnetic Pulses in Dispersive Media, J. Opt. Soc. Am. A, vol. 13, no. 6, pp. 1204-1217, 1996.
The Computation of Linear Dispersive Electromagnetic Waves, Applied Computational Electromagnetics Society Journal, invited paper in special issue titled ``Applied Mathematics: meeting the challenges presented by Computational Electromagnetics,´´ vol. 11, no. 1, pp. 8-16, 1996.
Analysis of Exponential Time-Differencing for FD-TD in Lossy Dielectrics, IEEE Transactions on Antennas and Propagation, vol. 45, no. 6, pp. 1054-1057, 1997.
A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell´s Equations with High-Order Staggered Finite Difference Schemes, J. Computational Physics, vol. 139, pp. 184-208, 1998.
On the Termination of the Perfectly Matched Layer with Local Absorbing Boundary Conditions, J. Computational Physics, vol. 143, pp. 665-673, 1998.
Plane-Wave Analysis and Comparison of Split-Field, Biaxial and Uniaxial PML Methods as ABCs for Pseudospectral Electromagnetic Wave Simulations in Curvilinear Coordinates, J. Computational Physics, vol. 146, pp. 747-774, 1998.
Performance Evaluation and Absorption Enhancement of the Grote-Keller and Unsplit PML Boundary Conditions for the 3-D FDTD Method in Spherical Coordinates, IEEE Transactions on Magnetics, vol. 35, no. 3, pp. 1418-1421, 1999.
Asymptotic and Energy Estimates for Electromagnetic Pulses in Dispersive Media: Addendum, J. Opt. Soc. Am. A, vol. 16, no. 11, pp. 2799-2800, 1999.
Reflectionless Sponge Layers as Absorbing Boundary Conditions for the Numerical Solution of Maxwell´s Equations in Rectangular, Cylindrical and Spherical Coordinates, SIAM J. Applied Mathematics, vol. 60, no. 3, pp. 1037-1058, 2000.
Reflectionless Sponge Layers for the Numerical Solution of Maxwell´s Equations in Cylindrical and Spherical Coordinates, Applied Numerical Mathematics, vol. 33, no. 1-4, pp. 517-524, 2000.
Numerical Dispersion and Absorbing Boundary Conditions, International Journal of Numerical Modelling: Devices, Circuits and Fields , vol. 13, no. 5, pp. 483-498, 2000. Special Issue titled ``ABC´s for CEM,´´ edited by P.G. Petropoulos.
A Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell´s Equations, J. Computational Physics , vol. 168, no. 2, pp. 286-315, 2001.
Nonlinear Stability of Electrified Fluid Sheets, Physics of Fluids, vol. 13, no. 12, pp. 3547-3563, 2001.
Approximating the Surface Impedance of a Homogeneous Lossy Half-Space: An Example of "Dialable" Accuracy, IEEE Transactions on Antennas and Propagation, vol. 50, no. 7, pp. 941-943, 2002.
The Effect of Electric Fields on the Rupture of Thin Viscous Films by van der Waals Forces,Physics of Fluids, vol. 15, no. 3, pp. 641-652, 2003.
An Analytical Study of the Discrete Perfectly Matched Layer for the Time-Domain Maxwell Equations in Cylindrical Coordinates,IEEE Transactions on Antennas and Propagation, vol. 51, no. 7, pp. 1671-1675, 2003.
On the Long-Time Behavior of Unsplit Perfectly Matched Layers,IEEE Transactions on Antennas and Propagation, vol. 52, no. 5, pp. 1335-1342, 2004.
Generation of Interfacial Instabilities in Charged Electrified Viscous Liquid Films, Journal of Engineering Mathematics, vol. 50, pp. 223-240, 2004.
Accurate and Efficient Boundary Integral Methods for Electrified Liquid Bridge Problems, SIAM J. Scientific Computing, vol. 26, no. 6, pp. 2102-2132, 2005.
On the Time-Domain Response of Cole-Cole Dielectrics,IEEE Transactions on Antennas and Propagation, vol. 53, no. 11, pp. 3741-3746, 2005.
Gravity Capillary Waves in Fluid Layers under Normal Electric Fields, Physical Review E, vol. 72, pp. 051601-1 to 051601-9, 2005.
Nonlinear Stability of a Charged Electrified Viscous Liquid Film Under the Action a Horizontal Electric Field, Physics of Fluids, vol. 18, no. 4, pp. 042102-1 to 042102-10, 2006.
Monodisperse Drop Formation in Square Microchannels, Physical Review Letters, vol. 96, no. 14, pp. 144501-1 to 144501-4, 2006.
Electrohydrodynamic Linear Stability of Two Immiscible Fluids in Channel Flow, Electrochimica Acta, vol. 51, no. 25,pp. 5316-5323, 2006.
Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel, J. Fluid Mech., vol. 583,pp. 347-377, 2007.
A Numerical Scheme to Simulate Electromagnetic Pulses Propagating in Cole-Cole Dielectrics, IEEE Transactions on Antennas and Propagation, submitted, 2006.
Reports and Conference Proceedings Publications
A Fourth-Order FD-TD Scheme for Electromagnetics, Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation, pp. 883-887, 2000.
The FD-TD Method: Theory and Applications, Applied Computational Electromagnetics: State of the Art and Future Trends, Vol. NATO-ASI Series: SERS. F, pp. 202-242, Springer-Verlag (2000).
A Non-Dissipative Staggered Fourth-Order Accurate Explicit Finite Difference Scheme for the Time-Domain Maxwell´s Equations, ICASE Technical Report, No. 99-30, NASA/CR-1999-209514, 1999.
Well-Posed Perfectly Matched Layers, Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, pp. 567-569, 1998.
A Comparison of the Grote-Keller ABC and the Unsplit PML for Maxwell´s Equations in Spherical Coordinates, 14th Annual Review of Progress in Applied Computational Electromagnetics Proceedings, vol. 2, pp. 623-680, Monterey, CA, March 1998. Paper in special session, titled ``ABCs: Theoretical and Numerical Implementation Issues,´´ organized by P. G. Petropoulos.
The Direct Problem in Ultra-Short Pulse Electromagnetic Wave Propagation and Scattering, USAF Armstrong Laboratory Technical Report, AL/OE-TR-1997-0109, 1997.
Fourth-Order Accurate Staggered Finite Difference Schemes for the Time-Dependent Maxwell Equations, Invited Paper in the Proceedings of the 13th Dundee Conference on Ordinary and Partial Differential Equations , Pitman Research Notes in Mathematics Series, #370, pp. 85-107, UK, 1997.
The Application of PML ABCs in High-Order FD-TD Schemes, 13th Annual Review of Progress in Applied Computational Electromagnetics Proceedings, vol. 2, pp. 884-891, Monterey, CA, March 1997. Paper in special session, titled ``PML:Theoretical and Numerical Implementation Issues,´´ co-organized by P.G. Petropoulos & A.C. Cangellaris.
High-Order Nondissipative Staggered Schemes for Maxwell´s Equations, IEEE-APS International Symposium Proceedings, vol. 1, pp. 114-117, Montreal, Canada, July 1997. Paper invited in special session titled ``Interdisciplinary Computational Electromagnetics.´´
Modeling Propagation and Scattering in Dispersive Dielectrics with FD-TD, 10th Annual Review of Progress in Applied Computational Electromagnetics Proceedings, vol. 1, pp. 3-9, Monterey, CA, 1994.
Wave Hierarchies for Propagation in Dispersive Electromagnetic Media, Second International Conference on Ultra-Wideband Short-Pulse Electromagnetics Proceedings, pp. 351-354, Plenum Press, 1994.
Domain Integral Equation Analysis of Scattering in Layered Dielectric Media, IEEE-APS International Symposium Proceedings, pp. 761-764, 1992.
Phase Error Control for FD-TD Type Methods, First International Conference on Ultra-Wideband Short-Pulse Electromagnetics Proceedings , pp. 359-366, Plenum Press, 1992.
Validation of UTRC 2D CEM Codes, United Technologies Research Center Internal Report, November 1990.