Related papers: Penalty Methods for the Hyperbolic System Modellin…
A new interior-exterior penalty method for solving quasi-variational inequality and pseudo-monotone operators arising in two-dimensional point contact problem has been analyzed and developed in discontinuous Galerkin finite volume method…
We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is…
Strong gradient regions in tokamaks, such as the pedestal or internal transport barriers, are regions of reduced turbulence where neoclassical transport can play a dominant role. However, standard neoclassical transport theory assumes that…
The idea of new diagnostics method for the small-scale irregular structures of magnetically confined plasma is suggested in the present paper. The method can be based on measurements of intensity attenuation of the normal sounding waves.…
A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during…
When a plasma disrupts in a tokamak, significant heat and electromagnetic loads are deposited onto the surrounding device components. These forces scale with plasma current and magnetic field strength, making disruptions one of the key…
Strong $E\times B$ plasma flow shear is beneficial for reducing turbulent transport. However, traditional methods of driving flow shear do not scale well to large devices such as future fusion power plants. In this paper, we use a large…
Two-fluid, three-dimensional, flux-driven, global, electromagnetic turbulence simulations carried out by using the GBS code are used to identify the main parameters controlling turbulent transport in the tokamak boundary and to delineate an…
We present a focused introduction to exact penalty methods for nonlinear programs and mathematical programs with equilibrium constraints (MPECs), emphasizing their connection to modern error bound theory. The goal is twofold. First, we…
In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…
This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…
We introduce a Machine Learning framework, HIPED (HeIght and width Predictor for Edge Dynamics), for predicting and optimizing pedestal and core performance in spherical tokamak plasmas. Trained on pedestal and core datasets from the third…
An antiproton plasma confined in a quasi-1D device is described in terms of a self-consistent fluid formulation using a variational approach. Unlike previous treatments, the use of the time-dependent variational method allows to retain the…
The edge turbulence model Hermes (Dudson et al., 2017 Plasma Phys. Control. Fusion 59 05401) is set up for plasma boundary simulations with an RF antenna, using parameters characteristic of a tokamak edge. Cartesian slab geometry is used…
In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a novel approach using periodic orbit theory to analyze plasma turbulence, identifying fundamental structures…
This paper studies the $d$-dimensional extension of a fictitious domain penalization technique that we previously proposed for Neumann or Robin boundary conditions. We apply Droniou's approach for non-coercive linear elliptic problems to…
The problem of avoiding saturation of the coil currents is critical in large tokamaks with superconducting coils like ITER. Indeed, if the current limits are reached, a loss of control of the plasma may lead to a major disruption.…
This paper is devoted to the numerical approximation of a nonlinear temperature balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…