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    A Time Marching Scheme for Solving Volume Integral Equations on Nonlinear Scatterers

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    Type
    Presentation
    Authors
    Bagci, Hakan cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2015-01-07
    Permanent link to this record
    http://hdl.handle.net/10754/624102
    
    Metadata
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    Abstract
    Transient electromagnetic field interactions on inhomogeneous penetrable scatterers can be analyzed by solving time domain volume integral equations (TDVIEs). TDVIEs are oftentimes solved using marchingon-in-time (MOT) schemes. Unlike finite difference and finite element schemes, MOT-TDVIE solvers require discretization of only the scatterers, do not call for artificial absorbing boundary conditions, and are more robust to numerical phase dispersion. On the other hand, their computational cost is high, they suffer from late-time instabilities, and their implicit nature makes incorporation of nonlinear constitutive relations more difficult. Development of plane-wave time-domain (PWTD) and FFT-based schemes has significantly reduced the computational cost of the MOT-TDVIE solvers. Additionally, latetime instability problem has been alleviated for all practical purposes with the development of accurate integration schemes and specially designed temporal basis functions. Addressing the third challenge is the topic of this presentation. I will talk about an explicit MOT scheme developed for solving the TDVIE on scatterers with nonlinear material properties. The proposed scheme separately discretizes the TDVIE and the nonlinear constitutive relation between electric field intensity and flux density. The unknown field intensity and flux density are expanded using half and full Schaubert-Wilton-Glisson (SWG) basis functions in space and polynomial temporal interpolators in time. The resulting coupled system of the discretized TDVIE and constitutive relation is integrated in time using an explicit P E(CE) m scheme to yield the unknown expansion coefficients. Explicitness of time marching allows for straightforward incorporation of the nonlinearity as a function evaluation on the right hand side of the coupled system of equations. Consequently, the resulting MOT scheme does not call for a Newton-like nonlinear solver. Numerical examples, which demonstrate the applicability of the proposed MOT scheme to analyzing electromagnetic interactions on Kerr-nonlinear scatterers will be presented.
    Conference/Event name
    Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)
    Additional Links
    http://mediasite.kaust.edu.sa/Mediasite/Play/307b27d4ec064dc89cd0e82665fbabf31d?catalog=ca65101c-a4eb-4057-9444-45f799bd9c52
    Collections
    Electrical and Computer Engineering Program; Presentations; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division; Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2015)

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