Volume Equivalence Principle (VEP)

The volume equivalence principle (VEP) is an extension to the method of moments (MoM) for modelling finite dielectric objects using a volume mesh (tetrahedra and cuboidal1 elements).

The volume equivalence principle (VEP) is not used by default and would only be used when the solution requires an alternative to the default surface equivalence principle (SEP). More basis functions are usually required compared to the surface equivalence principle (SEP), but neighbouring cuboids or tetrahedra may have differing electric and magnetic properties.

The VEP is associated with a volume mesh, and general usability is inhibited by the order O(N2..3) memory and CPU-time scaling with the number of unknowns N. There are however cases where the VEP is advantageous over the SEP or the FEM/MoM:
  • The formulation is stable at low frequencies.
  • The formulation is stable when modelling dielectrics with very high permittivity (high dielectric constant).
  • It displays good stability and convergence properties for an iterative solution with the MLFMM.
  • It is well-suited to inhomogeneous and thin dielectric bodies.
Note: Tetrahedral VEP is not supported together with other dielectric modelling methods (SEP, FEM, VEP with cuboids, special Green’s functions) or periodic boundary conditions (PBC).
1 Only supported in EDITFEKO