Exact Inverse Operator on Field Equations  

作　　者：Edwin Eugene Klingman Edwin Eugene Klingman(Cybernetic Micro Systems Inc., San Gregorio, CA, USA)

机构地区：[1]Cybernetic Micro Systems Inc., San Gregorio, CA, USA

出　　处：《Journal of Applied Mathematics and Physics》2020年第10期2213-2222,共10页应用数学与应用物理（英文）

摘　　要：Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.

关 键 词：Anti-Derivative Anti-Curl Operator Maxwell’s Equations Geometric Calculus Kasner Metric Green’s Function Biot-Savart Operator 

分 类 号：O17[理学—数学]