Marcella Bonazzoli

High-order finite elements in numerical electromagnetism: degrees of freedom and generators in duality

Explicit generators for high-order (r>1) scalar and vector finite element spaces generally used in numerical electromagnetism are presented and classical degrees of freedom, the so-called moments, revisited. Properties of these generators on simplicial meshes are investigated, and a general technique to restore duality between moments and generators is proposed. Algebraic and exponential optimal h- and r-error rates are numerically validated for high-order edge elements on the problem of Maxwell’s eigenvalues in a square domain.

Parallel preconditioners for high‐order discretizations arising from full system modeling for brain microwave imaging

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwells equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy.This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwells equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy.

Whole-microwave system modeling for brain imaging

In this paper, we present the results of a whole-system modeling of a microwave measurement prototype for brain imaging, consisting of 160 ceramic-loaded antennas working around 1 GHz. The modelization has been performed using open source FreeFem++ solver. Quantitative comparisons were performed using commercial software Ansys-HFSS and measurements. Coupling effects between antennas are studied with the empty system (without phantom) and simulations have been carried out with a fine numerical brain phantom model issued from scanner and MRI data for determining the sensitivity of the system in realistic configurations.

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

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++ solver.

High order edge finite element approximations for the time-harmonic Maxwell's equations

The time-harmonic Maxwells equations model the propagation of electromagnetic waves and are therefore fundamental equations for the simulation of many modern devices in everyday life. The numerical solution of these equations is hampered by some fundamental problems especially in the high frequency regime. Fine meshes have to be used in order to accurately represent the solution and also to avoid the pollution effect, which is very well known for the Helmholtz equations. We propose in this paper to address this problem by considering high order finite element approximations and in particular Whitney edge elements.

Parallel preconditioners for high-order discretizations arising from full system modeling for brain microwave imaging: Parallel preconditioners and high order elements for microwave imaging

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwells equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy.This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwells equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy.

Dispersion analysis of triangle-based Whitney element methods for electromagnetic wave propagation

We study the numerical dispersion/dissipation of a triangle-based edge Finite Element Method (edgeFEM) of degree r ≥ 1 when coupled with the Leap-Frog (LF) finite difference scheme to simulate the electromagnetic wave propagation over a structured triangulation of the 2D physical domain. The analysis addresses the discrete eigenvalue problem resulting from the approximation of the dispersion relation. First, we present semi-discrete dispersion graphs by varying the approximation degree r and the number of discrete points per wavelength. The fully-discrete ones are then obtained by varying also the time step. Numerical results for the edgeFEM, resp. edgeFEM-LF, are compared with those for the node Finite Element Method (nodeFEM), resp. nodeFEM-LF, applied to the considered problem.

Microwave tomography for brain stroke imaging

This paper 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 or Newton-like methods) with successive solutions of a direct problem. The solution direct requests an accurate modeling of the whole-microwave measurement system as well as the as the whole-head. Moreover, as the system will be used for detecting brain strokes (ischemic or hemorrhagic) and for monitoring during the treatment, running times for the reconstructions should be fast. The method used is based on high-order finite elements, parallel preconditioners with the Domain Decomposition method and Domain Specific Language with open source FreeFEM++ solver.

High Order Edge Elements for Electromagnetic Waves: Remarks on Numerical Dispersion

We recall one set of possible basis vector fields and two different sets of possible degrees of freedom, those related to “small-edges” and those defined by “moments”, for the Nedelec’s first family of high order edge elements. We thus address a dispersion analysis of the resulting methods, when the time-harmonic Maxwell’s equation for the electric field is discretized on a simplicial mesh.

Parallel preconditioners and high order elements for microwave imaging

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwells equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy.This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such complex imaging systems are computationally expensive since they require solving the direct problem of Maxwells equations several times. Moreover, wave propagation problems in the high frequency regime are challenging because a sufficiently high number of unknowns is required to accurately represent the solution. In order to use these algorithms in practice for brain stroke diagnosis, running time should be reasonable. The method presented in this paper, coupling high order finite elements and parallel preconditioners, makes it possible to reduce the overall computational cost and simulation time while maintaining accuracy.