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EM.Tempo

20 bytes added, 23:47, 27 August 2014
/* Anisotropic Materials */
[[EM.Cube]]'s [[FDTD Module]] allows you to define a general anisotropic material, whose constitutive [[parameters]], i.e. permittivity ('''&epsilon;'''), permeability ('''&mu;'''), electrical conductivity ('''&sigma;''') and magnetic conductivity ('''&sigma;<sub>m</sub>'''), are all tensorial in nature. Each constitutive parameter in this case is represented by a 3×3 matrix:
{||[[Image:FDTD16.png|thumb|300px|]]|}
A "'''Uniaxial'''" material is a special case of an anisotropic material whose constitutive [[parameters]] are all diagonal matrices. Specifying an anisotropic material as <u>'''Uniaxial'''</u> in the [[FDTD Module]] has a very important computational implication. There are six field update equations for uniaxial materials at each time steps: three for the electric field and three for the magnetic field. In this respect, a uniaxial material is similar to an isotropic dielectric material. On the other hand, a fully anisotropic material with non-zero off-diagonal constitutive matrix elements requires twelve update equations at each time step: three equations for the three components of each of the four vector fields '''E''', '''D''', '''H''' and '''B'''. As a result, the time loop for fully anisotropic materials takes much longer time than uniaxial materials.
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