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A challenging and fundamental research problem is the better understanding and control of the turbulent transport of heat in present-day tokamak fusion experiments. Recent developments in numerical methods along with enormous gains in…
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…
With the advent of the gyrokinetic formalism, recent developments in low-noise nonlinear $\delta f$ methods, and enormous gains in computing power, large-scale gyrokinetic simulations have become an important tool for improved understanding…
A new version of GBS (Ricci et al. Plasma Phys. Control. Fusion 54, 124047, 2012; Halpern et al. J. Comput. Phys. 315, 388-408, 2016; Paruta et al. Phys. Plasmas 25, 112301, 2018) is described. GBS is a three-dimensional, flux-driven,…
The properties of the boundary plasma in a tokamak are now recognized to play a key role in determining the achievable fusion power and the lifetimes of plasma-facing components. Accurate quantitative modeling and improved qualitative…
One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a B\'ezier surface based finite element method. This code produces a highly sparse…
A self-consistent model is presented for the simulation of a multi-component plasma in the tokamak boundary. A deuterium plasma is considered, with the plasma species that include electrons, deuterium atomic ions and deuterium molecular…
Machine learning algorithms often struggle to control complex real-world systems. In the case of nuclear fusion, these challenges are exacerbated, as the dynamics are notoriously complex, data is poor, hardware is subject to failures, and…
Challenging aspects of large-scale turbulent edge simulations in plasma physics include robust nonlinear solvers and efficient preconditioners. This paper presents recent advances in the scalable solution of nonlinear partial differential…
Within the MNPBEM toolbox, developed for the simulation of plasmonic nanoparticles using a boundary element method approach, we show how to include substrate and layer structure effects. We develop the methodology for solving Maxwell's…
In magnetically confined plasmas used in Tokamak, turbulence is responsible for specific transport that limits the performance of this kind of reactors. Gyrokinetic simulations are able to capture ion and electron turbulence that give rise…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
GX is a code for solving the nonlinear gyrokinetic system for low-frequency turbulence in magnetized plasmas, particularly tokamaks and stellarators. In GX, our primary motivation and target is a fast gyrokinetic solver that can be used for…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations. In particular, given a discrete trial space, the optimal test space induces a numerical scheme delivering the best…
Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a…
Nuclear fusion is an attractive source of energy because the fuel is abundant and it produces low levels of carbon emissions. The tokamak, which confines a plasma using magnetic fields, is the most mature nuclear fusion reactor concept.…
The development of a quasi-linear gyrokinetic transport model for tokamak plasmas, ultimately designed to provide physically comprehensive predictions of the time evolution of the thermodynamic relevant quantities, is a task that requires…
The penalization method is used to take account of obstacles, such as the limiter, in a tokamak. Because of the magnetic confinement of the plasma in a tokamak, the transport occurs essentially in the direction parallel to the magnetic…
This work suggests several methods of uncertainty treatment in multiscale modelling and describes their application to a system of coupled turbulent transport simulations of a tokamak plasma. We propose a method to quantify the usually…