The first of Calderón identities indicates that the operator of the electric field integral equation (EFIE) can potentially act as a preconditioner for itself. However, the discretization of this preconditioning operator via the boundary element method (BEM) requires constructing a dual space commonly defined on a barycentric refinement of the orginal mesh. This contribution introduces a novel Calderón strategy that leverages high-order quasi-Helmholtz projectors. Unlike the standard strategies, which are based on barycentric refinements, a dual space is obtained by combinating functions of higher order. This strategy allows the development of a discretization of the Calderón identity that is suitable for arbitrary order. The well-conditioning of the proposed formulation is investigated, and numerical results are presented to corroborate the theory.
On a Novel Calderón Preconditioning Strategy Based on High-Order Quasi-Helmholtz Projectors / Bourhis, Johann; Franzò, Damiano; Merlini, Adrien; Andriulli, Francesco P.. - ELETTRONICO. - (2024), pp. 700-703. (Intervento presentato al convegno International Conference on Electromagnetics in Advanced Applications (ICEAA) tenutosi a Lisbon (Portugal) nel 02-06 September 2024) [10.1109/iceaa61917.2024.10701907].
On a Novel Calderón Preconditioning Strategy Based on High-Order Quasi-Helmholtz Projectors
Johann Bourhis;Damiano Franzò;Francesco P. Andriulli
2024
Abstract
The first of Calderón identities indicates that the operator of the electric field integral equation (EFIE) can potentially act as a preconditioner for itself. However, the discretization of this preconditioning operator via the boundary element method (BEM) requires constructing a dual space commonly defined on a barycentric refinement of the orginal mesh. This contribution introduces a novel Calderón strategy that leverages high-order quasi-Helmholtz projectors. Unlike the standard strategies, which are based on barycentric refinements, a dual space is obtained by combinating functions of higher order. This strategy allows the development of a discretization of the Calderón identity that is suitable for arbitrary order. The well-conditioning of the proposed formulation is investigated, and numerical results are presented to corroborate the theory.File | Dimensione | Formato | |
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On_a_Novel_Caldern_Preconditioning_Strategy_Based_on_High-Order_Quasi-Helmholtz_Projectors (published version).pdf
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https://hdl.handle.net/11583/2993387