COMPUTATION OF NONLINEAR ELECTROMAGNETIC EFFECTS BY MEANS OF FREQUENCY-DOMAIN VOLUME-INTEGRAL EQUATIONS

THERE IS A NEED TO DEVELOP SPECIAL PURPOSE ALGORITHMS FOR SOLVING ELECTROMAGNETIC COUPLING AND SCATTERING PROBLEMS, THAT WILL TAKE ADVANTAGE OF RECENT ADVANCES IN COMPUTER TECHNOLOGY. TO THAT END WE PROPOSE A NOVEL ALGORITHM THAT IS BASED ON SOLVING NONLINEAR VOLUME-INTEGRAL EQUATIONS IN THE FREQUENCY-DOMAIN. THIS METHOD APPEARS TO OFFER SEVERAL ADVANTAGES OVER OTHER TECHNIQUES: (A) IT WILL ALLOW THE SOLUTION OF NONLINEAR COUPLING PROBLEMS IN A RATHER DIRECT MANNER, (B) IT WILL TAKE ADVANTAGES OF THE SPECIAL STRUCTURE OF THE MATRIX-OPERATOR, WHICH IS FOUR-DIMENSIONAL TOEPLITZ-HANKEL, BY USING CONJUGATE-GRADIENTS, FAST FOURIER TRANSFORMS, AND CONVOLUTIONS, (C) IT APPEARS TO BE AMENABLE TO SEVERAL NEW COMPUTER ARCHITECTURES AND HARDWARE, SUCH AS VECTOR-CONCURRENT PROCESSORS, DIGITAL SIGNAL PROCESSING (DSP) CHIPS THAT PERFORM FAST CONVOLUTIONS, TRANSPUTER, AND OTHER NETWORKING POSSIBILITIES, AND (D) IT WILL EXTEND ELECTROMAGNETIC CODES AND MODELS ALREADY BEING DEVELOPED FOR COMMERCIAL PURPOSES BY SABBAGH ASSOCIATES. THE RANGE OF PROBLEMS THAT CAN BE EFFICIENTLY SOLVED BY THE ALGORITHS, AND THE ASSOCIATED HARDWARE, IS EXPECTED TO BE QUITE LARGE, EXTENDING FROM LINEAR EMP COUPLING TO CABLES IN THE PRESENCE OF A CONDUCTIVE DIELECTRIC HALF-SPACE (GROUND), TO NONLINEAR EFFECTS PRODUCED BY ELECTROMAGNETIC ENVIRONMENTS. AS AN EXAMPLE OF THE LATTER, WE WOULD EXPECT TO BE ABLE TO MODEL, IN A VERY STRAIGHTFORWARD MANNER, THE PROBLEM OF AIR BREAKDOWN IN APERTURES THAT ARE ILLUMINATED BY AN ELECTROMAGNETIC PULSE.