Stéphane Balac
University of Rennes
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Featured researches published by Stéphane Balac.
Computer Physics Communications | 2013
Stéphane Balac; Fabrice Mahé
Abstract When solving certain evolution type PDEs such as the Schrodinger equation, the Interaction Picture method is a valuable alternative to Split-Step methods. The Interaction Picture method has good computational features when used together with the standard 4th order Runge–Kutta scheme (giving rise to the RK4-IP method). In this paper we present an embedded Runge–Kutta scheme with orders 3 and 4 with the aim to deliver an estimation of the local error for adaptive step-size control purposes in the Interaction Picture method. The corresponding ERK4(3)-IP method preserves the features of the RK4-IP method and provides a local error estimate at no significant extra cost.
Magnetic Resonance in Medicine | 2001
Stéphane Balac; Gabriel Caloz; Guy Cathelineau; B. Chauvel; J.D. de Certaines
Numerical simulation is a valuable tool for the study of magnetic susceptibility artifacts from metallic implants. A major difficulty in the simulation lies in the computation of the magnetic field induced by the metallic implant. A new method has been designed and implemented to compute the magnetic field induced by metallic objects of arbitrary shape. The magnetic field is expressed pointwise in terms of a surface integral. Efficient quadrature schemes are proposed to evaluate this integral. Finally, the method is linked to an artifact reconstruction model to simulate the images. Magn Reson Med 45:724–727, 2001.
Computer Methods in Biomechanics and Biomedical Engineering | 2000
Stéphane Balac; Gabriel Caloz
Abstract The technique used to recognise information in Magnetic Resonance Imaging (MRI) is based on electromagnetic fields. A linearly varying field (around 10−2 Tesla per meter) is added to a strong homogeneous magnetic field (order of magnitude of approximately one Tesla). When these fields are disturbed by the presence of a paramagnetic material, in the sample for instance, the resulting image is usually distorted, these distortions being termed artifacts. Our goal is to present a method, assuming the field disturbances are known, to construct the resulting images. A mathematical model of the MRI process is developed. The way the images are distorted in intensity and shape is explained and an algorithm to simulate magnetic susceptibility artifacts is deduced.
Mathematical and Computer Modelling | 2008
Stéphane Balac; Laurent Chupin
The technique used to spot information in Magnetic Resonance Imaging (MRI) uses electromagnetic fields. Even minor perturbations of these magnetic fields can disturb the imaging process and may render clinical images inaccurate or useless. Modelling and numerical simulation of the effects of static field inhomogeneities are now well established. Less attention has been paid to mathematical modelling of the effects of radio-frequency (RF) field inhomogeneities in the imaging process. When considering RF field inhomogeneities, the major difficulty is that the mathematical expression of the magnetisation vector is not anymore explicitly known in contrast with the unperturbed case. Indeed, the Bloch equation becomes an ordinary differential equation with nonconstant coefficients that cannot be solved analytically. The use of standard numerical schemes for ordinary differential equations to compute the magnetisation vector appears to be costly and not well suited for MRI image simulation. In this paper, we present an original method for solving the Bloch equation based on a truncated series expansion of the solution. The computational cost of the method reduces to the computation of the eigenelements of a block tridiagonal matrix of a very small size.
Mathematical and Computer Modelling | 2004
Stéphane Balac; Hugues Benoit-Cattin; T Lamotte; Christophe Odet
A method to compute the magnetic field induced by susceptibility inhomogeneities in magnetic resonance imaging is presented. It is based on a boundary integral representation formulae. The integral is set over the surfaces between media of different magnetic susceptibilities. The computational procedure consists of approximating these surfaces with triangular mesh elements and using analytical expressions to compute the integral over each triangle. The proposed method supplies high accuracy and is easily paralleled. A detailed analysis for the convergence rate of the method is performed. Numerical results obtained for several samples, including a human head, are presented.
IEEE Transactions on Magnetics | 2002
Stéphane Balac; Gabriel Caloz
We present an original method to compute the magnetic field generated by some electromagnetic device through the coupling of an integral representation formula and a finite-element method (FEM). The unbounded three-dimensional magnetostatic problem is formulated in terms of the reduced scalar potential. Through an integral representation formula, an equivalent problem is set in a bounded domain and discretized using a standard FEM. As a byproduct, an integral representation formula is proposed to compute the magnetic field in any point of the space from the reduced scalar potential without numerical differentiation.
Scientific Reports | 2016
Zeina Abdallah; Yann Boucher; Arnaud Fernandez; Stéphane Balac; Olivier Llopis
A microwave domain characterization approach is proposed to determine the properties of high quality factor optical resonators. This approach features a very high precision in frequency and aims to acquire a full knowledge of the complex transfer function (amplitude and phase) characterizing an optical resonator using a microwave vector network analyzer. It is able to discriminate between the different coupling regimes, from the under-coupling to the selective amplification, and it is used together with a model from which the main resonator parameters are extracted, i.e. coupling factor, intrinsic losses, phase slope, intrinsic and external quality factor.
Applied Numerical Mathematics | 2002
Stéphane Balac; Gabriel Caloz
A method to compute the magnetic field induced by a metallic body embedded in a uniform external field is presented. It is based on boundary integral representation formulae for the magnetic induction . A computational procedure is proposed which consists of using analytic expressions to compute the integral over the flat panels of the boundary and a piecewise quadratic interpolation of the surface for the curved panels. Superconvergence occurs in the latter case. The method supplies both high accuracy and low computation time, requirements that are not fulfilled when using standard numerical methods.
IEEE Transactions on Magnetics | 2003
Stéphane Balac; Gabriel Caloz
In computation of magnetostatic fields in regions containing current sources, it is classical to write the corresponding magnetostatic problem in terms of the reduced scalar magnetic potential /spl phi/. Usually numerical differentiation is used to obtain the magnetic field H from the potential values, which implies loss in accuracy. An alternative is to compute H from /spl phi/ by an integral formula. In fact, the formula does not give a straightforward solution because of a cancellation in the integral. In this paper, we investigate the mathematical reason why the formula is not suited for numerical purposes. We carry out a careful numerical analysis with illustrations on a test example and propose a way to circumvent this difficulty by using a sort of decomposition method.
Optics Letters | 2018
Pierre Guillemé; Julie Stervinou; Tony Rohel; Charles Cornet; David Gachet; Stéphane Balac; Fabrice Mahé; Yannick Dumeige; Yoan Léger
Whispering gallery mode resonators are key devices for integrated photonics. Despite their generalization in fundamental and applied science, information on spatial confinement of light in these structures is mostly retrieved from purely spectral analysis. In this work, we present a detailed spectral and spatial characterization of whispering gallery modes in active semiconductor microdisk resonators by use of hyperspectral cathodoluminescence. By comparing our experimental findings to finite element simulations, we demonstrate that the combination of spectral and spatial measurements enables unique identification of the modes and even reveals specific features of the microresonator geometry, such as a wedge profile.