scholarly journals An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation

2019 ◽  
Vol 146 (3) ◽  
pp. 2068-2079 ◽  
Author(s):  
Rui Chen ◽  
Sadeed Bin Sayed ◽  
Noha Alharthi ◽  
David Keyes ◽  
Hakan Bagci
Keyword(s):  
Integral Equation ◽  
Time Domain ◽  
The Time Domain ◽  
Kirchhoff Integral

scholarly journals Lightning Channel-Base Current Identification as Solution of a Volterralike Integral Equation

2008 ◽  
Vol 2 (1) ◽  
pp. 160-165 ◽  
Author(s):  
Federico Delfino ◽  
Renato Procopio ◽  
Mansueto Rossi
Keyword(s):  
Integral Equation ◽  
Numerical Simulations ◽  
Time Domain ◽  
Measurement Noise ◽  
Induction Field ◽  
Base Current ◽  
Lightning Channel ◽  
Regularization Techniques ◽  
Ill Conditioning ◽  
The Time Domain

In this paper, a novel procedure to reconstruct the lightning channel-base current starting from the measurement of the induction field generated by it is presented. The procedure is based on a suitable mathematical manipulation of the equation expressing the induction field in the time domain, in order to transform it into a Volterra-like integral equation. Such kind of equations can be easily numerically solved without resorting to any sort of regularization techniques as they are not affected by the typical ill-conditioning of the inverse problems. The developed algorithm has been validated by means of several numerical simulations, which have shown its effectiveness also in presence of measurement noise on the induction field values.

On the Dynamics of Large Systems With Localized Nonlinearities

1988 ◽  
Vol 55 (4) ◽  
pp. 946-951 ◽  
Author(s):  
P. Hagedorn ◽  
W. Schramm
Keyword(s):  
Integral Equation ◽  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Dynamic System ◽  
Frequency Response ◽  
Time Domain ◽  
Numerical Procedure ◽  
Linear Subsystem ◽  
Large Systems ◽  
The Time Domain

In this paper, a certain class of dynamical systems is discussed, which can be decomposed into a large linear subsystem and one or more nonlinear subsystems. For this class of nonlinear systems the dynamic behavior is represented in the time domain by means of an integral equation. A simple numerical procedure for the solution of this integral equation is given. It is also shown how the decomposition of the system can be used in measuring the frequency response of the large linear subsystem, without actually separating it from the nonlinear subsystems. An elastostatic analogy is used to illustrate the ideas and a numerical example is given for a dynamic system.

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