A new vision of numerical methods for the solution of Maxwell's equations related to the FD-TD method; application to general anisotropic media

1994 ◽  
Author(s):  
T. Materdey
Keyword(s):  
Numerical Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Anisotropic Media ◽  
New Vision

scholarly journals A New Formulation of Maxwell’s Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 868
Author(s):  
Simona Fialová ◽  
František Pochylý
Keyword(s):  
Numerical Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Control Volume ◽  
Control Volume Method ◽  
Integral Forms ◽  
New Formulation ◽  
Electrical Induction ◽  
Volume Method ◽  
Integral Identities

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.

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