This article deals with microwave tomography for brain stroke imaging using state-of-the-art numerical modeling and massively parallel computing. Iterative microwave tomographic imaging requires the solution of an inverse problem based on a minimization algorithm (e.g., gradient based) with successive solutions of a direct problem such as the accurate modeling of a whole-microwave measurement system. Moreover, a sufficiently high number of unknowns is required to accurately represent the solution. As the system will be used for detecting a brain stroke (ischemic or hemorrhagic) as well as for monitoring during the treatment, the running times for the reconstructions should be reasonable. The method used is based on high-order finite elements, parallel preconditioners from the domain decomposition method and domain-specific language with the opensource FreeFEM&#x0002B;&#x0002B; solver.

/pdf/numerical-modeling-and-high-speed-parallel-computing-new-57j9rw8rzh.pdf

Numerical Modeling and High-Speed Parallel Computing: New Perspectives on Tomographic Microwave Imaging for Brain Stroke Detection and Monitoring.

Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations

A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations

In this paper we introduce methods for electromagnetic wave propagation, based on splines and on T-splines. We define spline spaces which form a De Rham complex and, following the isogeometric paradigm, we map them on domains which are (piecewise) spline or NURBS geometries. We analyse their geometric structure, as related to the connectivity of the underlying mesh, and we give a physical interpretation of the fields degrees-of-freedom through the concept of control fields. The theory is then extended to the case of meshes with T-junctions, leveraging on the recent theory of T-splines. The use of T-splines enhance our spline methods with local refinement capability and numerical tests show the efficiency and the accuracy of the techniques we propose.

Isogeometric Methods for Computational Electromagnetics: B-spline and T-spline discretizations

Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

Low-order Whitney elements are widely used for electromagnetic field problems. Higher-order approximations are receiving increasing interest, but their definition remains unduly complex. In this paper we propose a new simple construction for Whitney $p$-elements of polynomial degree higher than one that use only degrees of freedom associated to $p$-chains. We provide a basis for these elements on simplicial meshes and give a geometrical localization of all degrees of freedom. Properties of the higher-order Whitney complex are deeply investigated.

/pdf/whitney-forms-of-higher-degree-5e2c78vtc5.pdf

Whitney Forms of Higher Degree

Homogenization of structured electromagnetic materials and metamaterials

We present a novel method for analyzing 2D and 3D lossy periodic composites materials, combining an asymptotic multiscale method combined with the unfolding method. The computed effective conductivity for square cylinders (2D), and cubes (3D) suspended in a host isotropic medium are compared with the Maxwell-Garnett mixing formula predictions. The electromagnetic field in a finite lattice of square cylinders using this novel technique is compared with the exact electromagnetic field calculated directly in the heterogeneous lattice.

http://ieeexplore.ieee.org/iel5/10686/33799/01610125.pdf

Effective constitutive parameters of periodic composites

A novel methodology to evaluate the effective parameters of a three-dimensional lattice of chiral inclusions is presented. The homogenization is based upon mathematical arguments. The finite element technique is used to compute the constitutive parameters.

Effective electromagnetic properties of structured chiral metamaterials

Different analytical and numerical methods for calculating the surface impedance of a high impedance surface (HIS) structure have been studied and compared. In this article, two new approaches are proposed for calculating the surface impedance for general 2D-spatial periodic HIS structures, which include both the symmetric and asymmetric planar structures. Different comparisons are made, among analytical, numerical and experimental results, to validate our numerical calculation.

Alain Bossavit

Papers

Whitney Forms of Higher Degree

Homogenization of structured electromagnetic materials and metamaterials

Effective constitutive parameters of periodic composites

Effective electromagnetic properties of structured chiral metamaterials

Surface impedance models for high impedance surfaces