Irwin Yousept
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View article: Numerical Analysis for a Hyperbolic PDE-Constrained Optimization Problem in Acoustic Full Waveform Inversion
Numerical Analysis for a Hyperbolic PDE-Constrained Optimization Problem in Acoustic Full Waveform Inversion Open
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the hyperbol…
View article: Numerical solutions to Hyperbolic Maxwell quasi-variational inequalities in Bean–Kim model for type-II superconductivity
Numerical solutions to Hyperbolic Maxwell quasi-variational inequalities in Bean–Kim model for type-II superconductivity Open
This paper is devoted to the finite element analysis for the Bean–Kim model governed by the full 3D Maxwell equations. Describing type-II superconductivity at the macroscopic level, this model leads to a challenging coupled system consisti…
View article: Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion
Analysis of the SQP Method for Hyperbolic PDE-Constrained Optimization in Acoustic Full Waveform Inversion Open
In this paper, the SQP method applied to a hyperbolic PDE-constrained optimization problem is considered. The model arises from the acoustic full waveform inversion in the time domain. The analysis is mainly challenging due to the involved…
View article: Eddy current approximation in Maxwell obstacle problems
Eddy current approximation in Maxwell obstacle problems Open
This paper analyzes the mathematical modeling of the transient eddy current approximation in the Maxwell obstacle problem. Here, the medium is assumed to be solely open, containing conducting and non-conducting materials with certain prope…
View article: Maxwell quasi-variational inequalities in superconductivity
Maxwell quasi-variational inequalities in superconductivity Open
This paper is devoted to the mathematical modeling and analysis of a hyperbolic Maxwell quasi-variational inequality (QVI) for the Bean-Kim superconductivity model with temperature and magnetic field dependence in the critical current. Our…
View article: Optimal control of elliptic variational inequalities with bounded and unbounded operators
Optimal control of elliptic variational inequalities with bounded and unbounded operators Open
This paper examines optimal control problems governed by elliptic variational inequalities of the second kind with bounded and unbounded operators. To tackle the bounded case, we employ the polyhedricity of the test set appearing in the du…
View article: Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities
Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities Open
This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape which minimizes a certain cost…
View article: Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion
Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion Open
Level Set--Based Shape Optimization Approach for Sharp-Interface Reconstructions in Time-Domain Full Waveform Inversion
View article: High-order homogenization in optimal control by the Bloch wave method
High-order homogenization in optimal control by the Bloch wave method Open
This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient A ε . The small parameter ε > 0 denotes the periodicity length.…
View article: LEVEL SET-BASED SHAPE OPTIMIZATION APPROACH FOR SHARP-INTERFACE RECONSTRUCTIONS IN TIME-DOMAIN FULL WAVEFORM INVERSION
LEVEL SET-BASED SHAPE OPTIMIZATION APPROACH FOR SHARP-INTERFACE RECONSTRUCTIONS IN TIME-DOMAIN FULL WAVEFORM INVERSION Open
Velocity models presenting sharp interfaces are highly relevant in seismic imaging, for instance for imaging the subsurface of the Earth in the presence of salt bodies. In order to mitigate the oversmoothing of classical regularization str…
View article: Oversmoothing Tikhonov regularization in Banach spaces <sup>*</sup>
Oversmoothing Tikhonov regularization in Banach spaces <sup>*</sup> Open
This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider the so-called oversmoothing state in the sense that the Tikhonov penalization is not able …
View article: Oversmoothing Tikhonov regularization in Banach spaces
Oversmoothing Tikhonov regularization in Banach spaces Open
This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider the so-called oversmoothing state in the sense that the Tikhonov penalization is not able …
View article: Variational source conditions in Lp-spaces
Variational source conditions in Lp-spaces Open
We propose and analyze variational source conditions (VSC) for the Tikhonov regularization method with Lp-norm penalties for a general ill-posed operator equation in a Banach space. Our analysis is based on the use of the celebrated Little…
View article: Well-posedness theory for electromagnetic obstacle problems
Well-posedness theory for electromagnetic obstacle problems Open
This paper develops a well-posedness theory for hyperbolic Maxwell obstacle problems generalizing the result by Duvaut and Lions (1976) [5]. Building on the recently developed result by Yousept (2020) [30], we prove an existence result and…
View article: Shape optimization for superconductors governed by H(curl)-elliptic\n variational inequalities
Shape optimization for superconductors governed by H(curl)-elliptic\n variational inequalities Open
This paper is devoted to the theoretical and numerical study of an optimal\ndesign problem in high-temperature superconductivity (HTS). The shape\noptimization problem is to find an optimal superconductor shape which minimizes\na certain c…
View article: Consistency of a phase field regularisation for an inverse problem governed by a quasilinear Maxwell system
Consistency of a phase field regularisation for an inverse problem governed by a quasilinear Maxwell system Open
An inverse problem of reconstructing the magnetic reluctivity in a quasilinear magnetostatic Maxwell system is studied. To overcome the ill-posedness of the inverse problem, we propose and investigate two regularisations posed as constrain…
View article: Fully Discrete Scheme for Bean's Critical-state Model with Temperature Effects in Superconductivity
Fully Discrete Scheme for Bean's Critical-state Model with Temperature Effects in Superconductivity Open
This paper examines the fully discrete analysis of a hyperbolic Maxwell-type variational inequality with temperature effects arising from Bean's critical-state model in type-II (high-temperature) superconductivity. Here, temperature depend…
View article: Variational source conditions for the reconstruction of distributed fluxes
Variational source conditions for the reconstruction of distributed fluxes Open
This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this inve…
View article: Variational source condition for ill-posed backward nonlinear Maxwell’s equations
Variational source condition for ill-posed backward nonlinear Maxwell’s equations Open
This paper analyzes the Tikhonov regularization for ill-posed backward nonlinear Maxwell's equations. We propose a variational source condition (VSC), leading to power-type convergence rates for the Tikhonov regularization. By means of the…
View article: Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity
Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity Open
This paper focuses on the numerical analysis for three-dimensional Bean's critical-state model in type-II superconductivity. We derive hyperbolic mixed variational inequalities of the second kind for the evolution Maxwell equations with Be…
View article: Optimal Control of Non-Smooth Hyperbolic Evolution Maxwell Equations in Type-II Superconductivity
Optimal Control of Non-Smooth Hyperbolic Evolution Maxwell Equations in Type-II Superconductivity Open
We analyze the optimal control of an electromagnetic process in type-II superconductivity. The PDE-constrained optimization problem is to find an optimal applied current density, which steers the electromagnetic fields to the desired ones …
View article: Edge Element Method for Optimal Control of Stationary Maxwell System with Gauss Law
Edge Element Method for Optimal Control of Stationary Maxwell System with Gauss Law Open
A novel edge element method is proposed for the optimal control of the stationary Maxwell system with a nonvanishing charge density. The proposed approach does not involve the usual saddle-point formulation and features a positive definite…
View article: A Posteriori Error Analysis for the Optimal Control of Magneto-Static\n Fields
A Posteriori Error Analysis for the Optimal Control of Magneto-Static\n Fields Open
This paper is concerned with the analysis and numerical analysis for the\noptimal control of first-order magneto-static equations. Necessary and\nsufficient optimality conditions are established through a rigorous Hilbert\nspace approach. …
View article: A Posteriori Error Analysis for the Optimal Control of Magneto-Static Fields
A Posteriori Error Analysis for the Optimal Control of Magneto-Static Fields Open
This paper is concerned with the analysis and numerical analysis for the optimal control of first-order magneto-static equations. Necessary and sufficient optimality conditions are established through a rigorous Hilbert space approach. The…
View article: Optimal control of the full time-dependent maxwell equations
Optimal control of the full time-dependent maxwell equations Open
This paper analyzes the optimal control of the full time-dependent Maxwell equations. Our goal is to find an optimal current density and its time-dependent amplitude which steer the electric and magnetic fields to the desired ones. The mai…
View article: Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model
Shape sensitivities for an inverse problem in magnetic induction tomography based on the eddy current model Open
In this paper the shape derivative of an objective depending on the solution of an eddy current approximation of Maxwell’s equations is obtained. Using a Lagrangian approach in the spirit of Delfour and Zolésio, the computation of the shap…
View article: Optimal bilinear control of eddy current equations with grad–div regularization
Optimal bilinear control of eddy current equations with grad–div regularization Open
An optimal bilinear control problem governed by time-harmonic eddy current equations is considered to estimate the electric conductivity of a 3D bounded isotropic domain. The model problem is mainly complicated by the possible presence of …