In this work, we present a quasi-Helmholtz projector-based preconditioning and stabilization of the time domain electric field integral equation when discretized with high-order basis functions and high-order convolution quadrature schemes. The proposed approach effectively cures the ill-conditioning at large time steps that the original scheme suffers from along with the late time instabilities caused by the static solenoidal nullspace. This stabilization is achieved through a generalization of the quasi-Helmholtz projectors adapted to the high-order space basis functions and the high-order implicit schemes used by the convolution quadrature method.

On the Regularization of the High Order Time Domain EFIE with Quasi-Helmholtz Projectors / Cordel, Pierrick; Bourhis, Johann; Franzò, Damiano; Merlini, Adrien; Andriulli, Francesco P.. - ELETTRONICO. - (2024), pp. 225-226. (Intervento presentato al convegno International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI) tenutosi a Firenze (Italy) nel 14-19 July 2024) [10.1109/ap-s/inc-usnc-ursi52054.2024.10686295].

On the Regularization of the High Order Time Domain EFIE with Quasi-Helmholtz Projectors

Pierrick Cordel;Johann Bourhis;Damiano Franzò;Francesco P. Andriulli
2024

Abstract

In this work, we present a quasi-Helmholtz projector-based preconditioning and stabilization of the time domain electric field integral equation when discretized with high-order basis functions and high-order convolution quadrature schemes. The proposed approach effectively cures the ill-conditioning at large time steps that the original scheme suffers from along with the late time instabilities caused by the static solenoidal nullspace. This stabilization is achieved through a generalization of the quasi-Helmholtz projectors adapted to the high-order space basis functions and the high-order implicit schemes used by the convolution quadrature method.
2024
979-8-3503-6990-8
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2993388