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In Physics and Mathematics, the Spacetime triangle diagram (STTD) technique, also known as the Smirnov method of incomplete separation of variables, refers to the direct space-time domain method for electromagnetic and scalar wave motion. == Basic stages == # (Electromagnetics) The system of Maxwell's equations is reduced to a second-order PDE for the field components, or potentials, or their derivatives. # The spatial variables are separated using convenient expansions into series and/or integral transforms—except one that remains bounded with the time variable, resulting in a PDE of hyperbolic type. # The resulting hyperbolic PDE and the simultaneously transformed initial conditions compose a problem, which is solved using the (Riemann-Volterra integral formula ). This yields the generic solution expressed via a double integral over a triangle domain in the bounded-coordinate—time space. Then this domain is replaced by a more complicated but smaller one, in which the integrant is essentially nonzero, found using a strictly formalized procedure involving specific spacetime triangle diagrams (see, e.g., Refs.〔 A.B. Utkin, ''Localized Waves Emanated by Pulsed Sources: The Riemann-Volterra Approach''. In: Hugo E. Hernández-Figueroa, Erasmo Recami, and Michel Zamboni-Rached (eds.) (Non-diffracting Waves. ) Wiley-VCH: Berlin, pp. 287-306 (2013) 〕〔 A.B. Utkin, ''Electromagnetic Waves Generated by Line Current Pulses''. In: (Wave Propagation. ) Ed. Andrey Petrin, InTech: Vienna, 〕〔 A.B. Utkin, (The Riemann-Volterra time-domain technique for waveguides: A case study for elliptic geometry. ) ''Wave Motion'' 49(2), 347-363 (2012), doi: 10.1016/j.wavemoti.2011.12.001 〕〔 V.V. Borisov, A.V. Manankova, A.B. Utkin, (Spherical harmonic representation of the electromagnetic field produced by a moving pulse of current density ), ''Journal of Physics A: Mathematical and General'' 29(15), 4493-4514 (1996), doi: 10.1088/0305-4470/29/15/020 〕). # In the majority of cases the obtained solutions, being multiplied by known functions of the previously separated variables, result in the expressions of a clear physical meaning (nonsteady-state modes). In many cases, however, more explicit solutions can be found summing up the expansions or doing the inverse integral transform. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spacetime triangle diagram technique」の詳細全文を読む スポンサード リンク
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