Note on transformation to general curvilinear coordinates for Maxwell's curl equations
نویسنده
چکیده
Maxwell’s curl equations are formulated in curvilinear non-orthogonal coordinates in three dimensions in a manner that enables to preserve conventional Cartesian mesh for the finite-difference schemes by means of mere redefinition of the permittivity and permeability coefficients. It is highlighted that in the previous works on this subject (Ward and Pendry 1996 J. Modern Opt. 43 773; 1998 Phys. Rev. B 58 7252) inaccurate transformation to curvilinear coordinates, rooted in questionable transformation laws assigned to electric and magnetic field vectors, led to physical dubiety of the final formulae. In this note the amended equations are presented, capable of being easily adopted for the accurate finite-difference time-domain (FDTD) modelling of electromagnetic propagation and scattering problems in complicated geometries within the existing computational codes. PACS numbers: 03.50.De, 02.70.Bf Note on transformation to general curvilinear coordinates for Maxwell’s. . . 2
منابع مشابه
2 5 Ju l 2 00 7 Note on transformation to general curvilinear coordinates for Maxwell ’ s curl equations ( Is the magnetic field vector ‘ axial ’ ? )
Arguments for H and B to be considered 'axial', or pseudo vectors, are revisited. As a point against, we examine the complex-coordinate method for numerical grid truncation and mode loss analysis proved very successful in computational electrodynamics. This method is not compatible with convention that H and B are axial.
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