Calderón Strategies for the Convolution Quadrature Time Domain Electric Field Integral Equation

Pierrick Cordel (1) , Alexandre Dély (1) , Adrien Merlini (2, 3) , Francesco Andriulli (1)

1 DET - Department of Electronics and Telecommunications = DET Dipartimento di Elettronica e Telecomunicazioni [Politecnico di Torino]
2 Lab-STICC_PIM - Equipe PIM
3 IMT Atlantique - MO - Département Micro-Ondes

In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard schemes based on the electric field integral equation (EFIE). The standard time-domain EFIE-based approaches typically yield matrices that become increasingly illconditioned as the time-step or the mesh discretization density increase and suffer from the well-known DC instability. This work presents solutions to these issues that are based both on new Calder´on strategies and quasi-Helmholtz projectors regularizations. In addition, to ensure an efficient computation of the marchingon- in-time, the proposed schemes leverage properties of the Z-transform—involved in the convolution quadrature discretization scheme—when computing the stabilized operators. The two resulting formulations compare favorably with standard, well-established schemes. The properties and practical relevance of these new formulations will be showcased through relevant numerical examples that include canonical geometries and more complex structures.

Domaines: Physique Numérique [physics.comp-ph]

Pierrick Cordel, Alexandre Dély, Adrien Merlini, Francesco Andriulli. Calderón Strategies for the Convolution Quadrature Time Domain Electric Field Integral Equation. IEEE Open Journal of Antennas and Propagation, 2024, 1, pp.1-1. ⟨10.1109/OJAP.2024.3354044⟩. ⟨hal-04405445⟩