arXiv subjects

A. Merlini

Publications and source records attributed to A. Merlini.

5 recordsLinked to original sources

arXiv2026

High-Frequency Preconditioners for Electromagnetic Integral Equations Based on Helmholtz Regularizations

The numerical solution of the Electric Field Integral Equation (EFIE) via the Boundary Element Method (BEM) can be computationally challenging due to conditioning issues arising in different regimes, such as (i) when the frequency decreases and the discretization density remains constant, (ii) when the frequency is kept constant while the discretization is refined, and (iii) when the frequency increases along with the discretization density. To address these issues, several preconditioning approaches for the related matrix system have been developed in the literature, only a few of which address all regimes simultaneously. This paper investigates one of these techniques and presents a strategy for accelerating the associated matrix-vector products (MVPs). In particular, we propose a novel preconditioning strategy for the shifted Helmholtz operator, for which standard pseudo-inversion techniques have shown unsatisfactory results. Instead, the application of our preconditioning technique stabilizes the number of iterations in all the aforementioned regimes. In view of these achievements, the pseudo-inversion of the shifted Helmholtz operator can be obtained in quasi-linear complexity when proper acceleration strategies are used, thus enabling the numerical solution of the EFIE with the same complexity.

cs.CE↗

arXiv2026

Asymptotic Spectral Insights Behind Fast Direct Solvers for High-Frequency Electromagnetic Integral Equations on Non-Canonical Geometries

Integral-equation-based fast direct solvers for electromagnetic scattering can substantially reduce computational costs, especially in the presence of multiple excitations. We recently proposed a new high-frequency fast direct solver strategy that combines preconditioning techniques with acceleration algorithms. However, the validity of this approach applied to non-canonical geometries requires further justification. In this contribution, we collect relevant semiclassical microlocal results and use them to assess the legitimacy and effectiveness of the proposed fast direct solver in the high-frequency regime.

math.NA↗

arXiv2025

Spectral Analysis of Discretized Boundary Integral Operators in 3D: a High-Frequency Perspective

When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately equal to a fraction of the wavelength $\lambda$ of the incident wave, e.g., $\lambda/10$. In this work, by analyzing the spectra of the operator matrices, we show a discrepancy with respect to the continuous operators which grows with the simulation frequency, challenging the common belief that the aforementioned widely used discretization approach is sufficient to maintain the accuracy of the solution constant when increasing the frequency.

cs.CE↗

arXiv2024

Low-Frequency Stabilizations of the PMCHWT Equation for Dielectric and Conductive Media: On a Full-Wave Alternative to Eddy-Current Solvers

We propose here a novel stabilization strategy for the PMCHWT equation that cures its frequency and conductivity related instabilities and is obtained by leveraging quasi-Helmholtz projectors. The resulting formulation is well-conditioned in the entire low-frequency regime, including the eddy current one, and can be applied to arbitrarily penetrable materials, ranging from dielectric to conductive ones. In addition, by choosing the rescaling coefficients of the quasi-Helmholtz components appropriately, we prevent the typical loss of accuracy occurring at low frequency in the presence of inductive and capacitive type magnetic frill excitations, commonly used in circuit modeling to impose a potential difference. Finally, leveraging on quasi-Helmholtz projectors instead than on the standard Loop-Star decomposition, our formulation is also compatible with most fast solvers and is amenable to multiply connected geometries, without any computational overhead for the search for the global loops of the structure. The efficacy of the proposed preconditioning scheme when applied to both simply and multiply connected geometries is corroborated by numerical examples.

math.NA↗

arXiv2024

On a High-Frequency Analysis of Some Relevant Integral Equations in Electromagnetics

In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular, a comparison with the eigenvalues of the continuous operators will be presented that highlights deviations in the high frequency regime and impacts, in a peculiar way, the accuracy of the numerical solutions of each formulation. A study and a proactive analysis of numerical results from standard boundary element solvers and the predictions from the theoretical analysis will corroborate the analytical framework employed and the validity of our observations.

cs.CE↗