A Calderon Multiplicative Preconditioner for the PMCHWT Integral Equation

作者：Cools Kristof^*; Andriulli Francesco P; Michielssen Eric

来源：IEEE Transactions on Antennas and Propagation, 2011, 59(12): 4579-4587.

DOI：10.1109/TAP.2011.2165465

• Boundary integral equations
• Calderon multiplicative preconditioning
• dense discretization breakdown
• penetrable objects
• Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) equation

Electromagnetic scattering by penetrable bodies often is modelled by the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) integral equation. Unfortunately the spectrum of the operator involved in this equation is bounded neither from above or below. This implies that the equation suffers from dense discretization breakdown; that is, the condition numbers of the matrix resulting upon discretizing the equation rise with the mesh density. The electric field integral equation, often used to model scattering by perfect electrically conducting bodies, is susceptible to a similar breakdown phenomenon. Recently, this breakdown was cured by leveraging the Calderon identities. In this paper, a Calderon preconditioned PMCHWT integral equation is introduced. By constructing a Calderon identity for the PMCHWT operator, it is shown that the new equation does not suffer from dense discretization breakdown. A consistent discretization scheme involving both Rao-Wilton-Glisson and Buffa-Christiansen functions is introduced. This scheme amounts to the application of a multiplicative matrix preconditioner to the classical PMCHWT system, and therefore is compatible with existing boundary element codes and acceleration schemes. The efficiency and accuracy of the algorithm are corroborated by numerical examples.

• 出版日期2011-12