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Calderon preconditioning has also been used to regularize PMCHWT formulation in the case of homogeneous isotropic and chiral objects [118,119].
Michielssen, "A Calderon multiplicative preconditioner for the PMCHWT integral equation," IEEE Trans.
Michielssen, "A Caldern multiplicative preconditioner for the PMCHWT equation for scattering by chiral objects," IEEE Trans.
To avoid further confusion, we have used their old names, PMCHWT and CNF.
CMP-PMCHWT stands for the Calderon matrix multiplicative preconditioned PMCHWT formulation and [Laplace] is the edge length of a cube.
Here CMP-EFIE and CMP-PMCHWT stand for the Calderon matrix multiplicative preconditioned PEC-EFIE and PMCHWT formulations, respectively.
For a cube with high-dielectric contrast, both RWG and div-TO discretizations of the Muller-formulation show a bigger deviation with respect to PMCHWT, which shows a stable trend of convergence in any case.
This is especially remarkable for CTF and PMCHWT formulations, for which stable error curves described by small error values have been obtained when losses are present, providing more accurate results than the CNF and JMCFIE formulations for these cases.
However, the PMCHWT high error rate attained when using the iterative solver strongly differs with the 2% that would be obtained by means of direct solving.
Also the PMCHWT error shoots up absolutely in this particular case when direct solving is applied.
The iterative convergence of PMCHWT is still bad but, as occurred in the previous unmatched lossless case ([[epsilon].sub.r] = -3, [[mu].sub.r] = -1), direct solving by means of this formulation in these lossy cases gives error rates comparable to CTF data.
While JMCFIE and CNF formulations maintain almost invariable the response given for the ideal matched case, an evident improvement of the CTF and PMCHWT iterative parameters can be observed.
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