Calderón Preconditioners for the Global Multi-Trace Vector Potential Integral Equation

Calderón preconditioners for the global multi-trace Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT)-like formulation for the vector potential are presented. The technique is applicable to multi-domain structures containing multi-material junctions and possibly both PEC and homogeneous domains. A domain diagonal and a trace-type diagonal preconditioner are compared, which both show an iteration count independent of the mesh density in a global multi-trace configuration. The trace kind diagonal preconditioner is modified to obtain low-frequency-stable results, whereas the domain-diagonal preconditioner is automatically low-frequency stable. The number of iterations for the Calderón preconditioned multi-trace vector potential integral equations is not affected by the low-frequency and the dense-discretization breakdown, making the proposed preconditioners an excellent modeling tool to compute the fields over a broad spectrum of frequencies and meshes.