Adrien Merlini

IMT Atlantique | IMT

p>The electric field integral equation (EFIE) is known to suffer from ill-conditioning and numerical instabilities at low frequencies (low-frequency breakdown). A common approach to solve this problem is to rely on the loop and star decomposition of the unknowns. Unfortunatelly, building the loops is challenging in many applications, especially in...

p>The electric field integral equation (EFIE) is known to suffer from ill-conditioning and numerical instabilities at low frequencies (low-frequency breakdown). A common approach to solve this problem is to rely on the loop and star decomposition of the unknowns. Unfortunatelly, building the loops is challenging in many applications, especially in...

p>The electric field integral equation (EFIE) is known to suffer from ill-conditioning and numerical instabilities at low frequencies (low-frequency breakdown). A common approach to solve this problem is to rely on the loop and star decomposition of the unknowns. Unfortunatelly, building the loops is challenging in many applications, especially in...

Quasi-Helmholtz decompositions are fundamental tools in integral equation modeling of electromagnetic problems because of their ability of rescaling solenoidal and non-solenoidal components of solutions, operator matrices, and radiated fields. These tools are however incapable, per se, of modifying the refinement-dependent spectral behavior of the...

We present a Calder\'on preconditioning scheme for the symmetric formulation of the forward electroencephalographic (EEG) problem that cures both the dense discretization and the high-contrast breakdown. Unlike existing Calder\'on schemes presented for the EEG problem, it is refinement-free, that is, the electrostatic integral operators are not dis...

Time‐Domain Integral Equations discretized by the Time‐Domain Boundary Element Methods are a key technology when dealing with simulation scenarios including wideband devices and non‐linearities. The discretization in time of these integral equations can be obtained by a space‐time Galerkin approach or by leveraging on a convolution quadrature (CQ)...

This paper focuses on fast direct solvers for integral equations in the low-to-moderate-frequency regime obtained by leveraging preconditioned first kind or second kind operators regularized with Laplacian filters. The spectral errors arising from boundary element discretizations are properly handled by filtering that, in addition, allows for the u...

Brain-Computer Interfaces (BCIs) based on Steady State Visually Evoked Potentials (SSVEPs) have proven effective and provide significant accuracy and information-transfer rates. This family of strategies, however, requires external devices that provide the frequency stimuli required by the technique. This limits the scenarios in which they can be a...

The inverse source problem in electromagnetics has proved quite relevant for a large class of applications. In antenna diagnostics in particular, Love solutions are often sought at the cost of an increase of the dimension of the linear system to be solved. In this work, instead, we present a reduced-in-size single current formulation of the inverse...

Inverse source approaches have shown their relevance for several applications in the past years. They rely on the solution of an ill-posed problem where near-field/current data is reconstructed starting from far-field (or less informative field) information. Standard strategies, including the physically constrained ones using Love conditions, resul...

This work focuses on a quasi-linear-in-complexity strategy for a hybrid surface-wire integral equation solver for the electroencephalography forward problem. The scheme exploits a block diagonally dominant structure of the wire self block -- that models the neuronal fibers self interactions -- and of the surface self block -- modeling interface pot...

Brain-Computer Interfaces (BCIs) based on Steady State Visually Evoked Potentials (SSVEPs) have proven effective and provide significant accuracy and information-transfer rates. This family of strategies, however, requires external devices that provide the frequency stimuli required by the technique. This limits the scenarios in which they can be a...

Several strategies are available for solving the inverse source problem in electromagnetics. Among them, many have been focusing in retrieving Love currents by solving, after regularization, for Love's electric and magnetic currents. In this work we present a dual-element discretization, analysis, and stabilization of an inverse source formulation...

Widely employed for the accurate solution of the electroencephalography forward problem, the symmetric formulation gives rise to a first kind, ill-conditioned operator ill-suited for complex modelling scenarios. This work presents a novel preconditioning strategy based on an accurate spectral analysis of the operators involved which, differently fr...

In this paper we present a new regularized electric flux volume integral equation (D-VIE) for modeling high-contrast conductive dielectric objects in a broad frequency range. This new formulation is particularly suitable for modeling biological tissues at low frequencies, as it is required by brain epileptogenic area imaging, but also at higher one...

This paper extends the concept of Laplacian filtered quasi-Helmholtz decompositions we have recently introduced, to the basis-free projector-based setting. This extension allows the discrete analyses of electromagnetic integral operators spectra without passing via an explicit Loop-Star decomposition as previously done. We also present a fast schem...

This work focuses on the preconditioning and DC stabilization of the time domain electric field integral equation discretized in time with the convolution quadrature method. The standard formulation of the equation suffers from severe ill-conditioning for large time steps and refined meshes, in addition to DC instabilities plaguing standard solutio...

Integral equation formulations are a competitive strategy in computational electromagnetics but, lamentably, are often plagued by ill-conditioning and by related numerical instabilities that can jeopardize their effectiveness in several real case scenarios. Luckily, however, it is possible to leverage effective preconditioning and regularization st...

In this paper we present a new regularized electric flux volume integral equation (D-VIE) for modeling high-contrast conductive dielectric objects in a broad frequency range. This new formulation is particularly suitable for modeling biological tissues at low frequencies, as it is required by brain epileptogenic area imaging, but also at higher one...

Fast and accurate resolution of electromagnetic problems via the \ac{BEM} is oftentimes challenged by conditioning issues occurring in three distinct regimes: (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 inc...

Despite its several qualities, the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) formulation for simulating scattering by dielectric media suffers from numerical instabilities and severe ill-conditioning at low frequencies. While this drawback has been the object of numerous solution attempts in the standard low-frequency breakdown regime for sca...

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following shortcomings: (i) ill-conditioning when the frequency is low; (ii) ill-conditioning when the discretization density is high; (iii) ill-conditioning when the structure contains global loops (which are computationally e...

Solving the electroencephalography (EEG) forward problem is a fundamental step in a wide range of applications including biomedical imaging techniques based on inverse source localization. State-of-the-art electromagnetic solvers resort to a computationally expensive volumetric discretization of the full head to account for its complex and heteroge...

Solving the electroencephalography (EEG) forward problem is a fundamental step in a wide range of applications including biomedical imaging techniques based on inverse source localization. State-of-the-art electromagnetic solvers resort to a computationally expensive volumetric discretization of the full head to account for its complex and heteroge...

Eddy currents are central to several industrial applications and there is a strong need for their efficient modeling. Existing eddy current solution strategies are based on a quasi-static approximation of Maxwell's equations for lossy conducting objects and thus their applicability is restricted to low frequencies. On the other hand, available full...

Source localization based on electroencephalography (EEG) has become a widely used neuroimaging technique. However its precision has been shown to be very dependent on how accurately the brain, head and scalp can be electrically modeled within the so-called forward problem. The construction of this model is traditionally performed by leveraging Fin...

Source localization based on electroencephalography (EEG) has become a widely used neuroimagining technique. However its precision has been shown to be very dependent on how accurately the brain, head and scalp can be electrically modeled within the so-called forward problem. The construction of this model is traditionally performed by leveraging F...

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following problems: (i) ill-conditioning when the frequency is low; (ii) ill-conditioning when the discretization density is high; (iii) ill-conditioning when the structure contains global loops (which are computationally expen...

In computational electromagnetics, boundary integral equations are the scheme of choice for solving extremely large forward electromagnetic problems due to their high efficiency. However, two of the most used of these formulations, the electric and combined field integral equations (EFIE and CFIE), suffer from stability issues at low frequency and...

Brain-computer interface (BCI) methods are commonly studied using electroencephalogram (EEG) data recorded from human experiments. For understanding and developing BCI signal processing techniques, real data is costly to obtain and its composition is a priori unknown. The brain mechanisms generating the EEG are not directly observable and their sta...

Pythran is an open source static compiler that turns modules written in a subset of Python language into native ones. Assuming that scientific modules do not rely much on the dynamic features of the language, it trades them for powerful, possibly inter-procedural, optimizations. These optimizations include detection of pure functions, temporary all...