Changes

Steady-State Thermal Analysis

12 bytes added, 01:20, 17 June 2018
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[[Image:FD 7Point7PointA.png|thumb|left|480px| The 7-point computational molecule used by the finite difference solver.]]
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<math> T(i,j,k) = \frac{1}{6} \big[ T(i+1,j,k) + T(i-1,j,k) + T(i,j+1,k) + T(i,j-1,k) + T(i,j,k+1) + T(i,j,k-1) \big] </math>
Two standard types of domain boundary conditions can be appliedtake the following forms:
*Dirichlet boundary condition: &psi; T = k =const.*Neumann boundary condition: &part;&psi;T/&part;n = k = const.
In the above, &part;&psi;/&part;n denotes the normal derivative of the potential at the surface of the domain boundary. [[EM.Ferma]]'s default domain boundary condition for both the electrostatic and magnetostatic solvers is Dirichlet. At the interface between different material media, additional boundary conditions must be applied. These boundary conditions involve electric or magnetic field components. The field components can be expressed as partial derivatives of the potential, i.e. in the form of &part;&psi;/&part;x, &part;&psi;/&part;y or &part;&psi;/&part;z. Using the respective finite difference approximations of these derivatives, one arrives at fairly complicated difference equations involving the constitutive parameters &epsilon;, &mu; and &sigma;, which must be solved simultaneously with the primary potential difference equations.
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