Microwave tomographic imaging of cerebrovascular accidents by using high-performance computing

Tournier, Pierre-Henri; Aliferis, Iannis; Bonazzoli, Marcella; Buhan, Maya de; Darbas, Marion; Dolean, Victorita; Hecht, Frédéric; Jolivet, Pierre; Kanfoud, Ibtissam El; Migliaccio, Claire; Nataf, Frédéric; Pichot, Christian; Semenov, Serguei

doi:10.1016/j.parco.2019.02.004

Cited by 34 publications

(33 citation statements)

References 18 publications

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“…As an example of a practical problem with ξ prob > 0, we consider the modeling of a microwave imaging system, for the detection and monitoring of brain strokes. The prototype in Figure 1 was developed by the company EMTensor GmbH and studied in the framework of the ANR project MEDIMAX [76]. In the full application, the data acquired with this device are used as input for an inverse problem associated with the time-harmonic Maxwell's equations (1.1), which makes it possible to estimate the complex electric permittivity ε σ := ε + i σ/ω of the brain tissues of a patient affected by a stroke (observe that, with this definition, the coefficient µ(εω 2 + iσω) in (1.1) can be rewritten as ω 2 µε σ ).…”

Section: 4mentioning

confidence: 99%

Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

et al. 2019

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This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is constructed using Additive Schwarz domain decomposition methods. The theory developed here shows that if the absorption is large enough, and if the subdomain and coarse mesh diameters and overlap are chosen appropriately, then the classical two-level overlapping Additive Schwarz preconditioner (with PEC boundary conditions on the subdomains) performs optimally -in the sense that GMRES converges in a wavenumberindependent number of iterations -for the problem with absorption. An important feature of the theory is that it allows the coarse space to be built from low-order elements even if the PDE is discretised using high-order elements. It also shows that additive methods with minimal overlap can be robust. Numerical experiments are given that illustrate the theory and its dependence on various parameters. These experiments motivate some extensions of the preconditioners which have better robustness for problems with less absorption, including the propagative case. At the end of the paper we illustrate the performance of these on two substantial applications; the first (a problem with absorption arising from medical imaging) shows the empirical robustness of the preconditioner against heterogeneity, and the second (scattering by a COBRA cavity) shows good scalability of the preconditioner with up to 3,000 processors.

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Section: 4mentioning

confidence: 99%

Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

et al. 2019

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“…The algebraic formulation of optimized Schwarz methods, of the type of (12), was introduced in [31]. The implementation of the partition of unity in FreeFem++ is described in [32]: suitable piecewise linear functions χ s giving a continuous partition of unity ( N sub s=1 χ s = 1) are interpolated at the barycenters of the support (edge, face, volume) of each dof of the (high order) edge finite elements. This interpolation is obtained thanks to an auxiliary FreeFem++ scalar FE space (Edge03ds0, Edge13ds0, Edge23ds0) that has only the interpolation operator and no basis functions, available in the plugin Element Mixte3d mentioned before.…”

Section: Interpolation Operator For D = 3 R =mentioning

confidence: 99%

An example of explicit implementation strategy and preconditioning for the high order edge finite elements applied to the time-harmonic Maxwell’s equations

Bonazzoli¹,

Dolean

Hecht³

et al. 2018

Computers & Mathematics with Applications

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In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations. The implementation of high order curl-conforming finite elements is quite delicate, especially in the three-dimensional case. Here, we explicitly describe an implementation strategy, which has been embedded in the open source finite element software FreeFem++ (http://www.freefem.org/ff++/). In particular, we use the inverse of a generalized Vandermonde matrix to build a basis of generators in duality with the degrees of freedom, resulting in an easy-to-use but powerful interpolation operator. We carefully address the problem of applying the same Vandermonde matrix to possibly differently oriented tetrahedra of the mesh over the computational domain. We investigate the preconditioning for Maxwell's equations in the time-harmonic regime, which is an underdeveloped issue in the literature, particularly for high order discretizations. In the numerical experiments, we study the effect of varying several parameters on the spectrum of the matrix preconditioned with overlapping Schwarz methods, both for 2d and 3d waveguide configurations.

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“…This work has been motivated by biomedical applications, and in particular by the microwave imaging of cerebrovascular accidents [32,33]. Strokes are characterized by dielectric properties which are slightly altered (±10%) from that of a healthy brain.…”

Section: Concluding Remarks and Prospectsmentioning

confidence: 99%

“…in medical imaging, geophysical exploration or nondestructive testing. For instance, microwave imaging (electromagnetic high frequencies) is under investigation for cancer screening or brain stroke detection (see Tournier et al [32,33]). Numerical methods that are able to highlight dielectric contrast between normal and possibly abnormal tissue are of interest.…”

Section: Introductionmentioning

confidence: 99%

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Numerical resolution of an electromagnetic inverse medium problem at fixed frequency

Buhan

Darbas

2017

Computers & Mathematics with Applications

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The aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency. The governing equations are the time-harmonic Maxwell equations formulated in electric field in a two-dimensional bounded domain. We express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields. Our numerical reconstruction algorithm combines the BFGS method and an iterative process, called the Adaptive Eigenspace Inversion. The unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator. Both the eigenspace and the mesh are iteratively adapted during the minimization procedure. Numerical experiments illustrate the performance of the reconstruction for various configurations.

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Microwave tomographic imaging of cerebrovascular accidents by using high-performance computing

Cited by 34 publications

References 18 publications

Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption

An example of explicit implementation strategy and preconditioning for the high order edge finite elements applied to the time-harmonic Maxwell’s equations

Numerical resolution of an electromagnetic inverse medium problem at fixed frequency

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