A DC-Stable, Well-Balanced, Calderón Preconditioned Time Domain Electric Field Integral Equation


The marching-on-in-time (MOT) resolution of the time domain electrical field integral equation (TD-EFIE) has historically suffered from a variety of issues, together with: 1) instability; 2) spurious static contributions plaguing the answer; 3) low-frequency breakdown; and 4) dense discretization breakdown. The first issue can be resolved by using proper space-time Galerkin discretization schemes and correct quadrature methods. The second and the third issue are resolved by the quasi-Helmholtz Projected TD-EFIE (qHP-TDEFIE). This contribution introduces a multiplicative preconditioner which will be applied to the qHP-TDEFIE, without more modifying the original scheme. This preconditioner is predicated on Calderón techniques and guarantees that the MOT system will be solved efficiently using iterative methods, not solely for massive time step sizes however also for dense spatial discretizations, and for both merely and multiply connected geometries.

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