Related papers: Towards Robust Solvers for Nuclear Fusion Simulati…
Computing the solution of linear systems of equations is invariably the most time consuming task in the numerical solutions of PDEs in many fields of computational science. In this study, we focus on the numerical simulation of…
We present the lowest-order hybridizable discontinuous Galerkin schemes with numerical integration (quadrature), denoted as HDG-P0, for the reaction-diffusion equation and the generalized Stokes equations on conforming simplicial meshes in…
Shattered pellet injection (SPI) is selected for the disruption mitigation system in ITER, due to deeper penetration, expected assimilation efficiency and prompt material delivery. This article describes non-linear magnetohydrodynamic (MHD)…
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…
Entity resolution (ER) is a fundamental task in data integration that enables insights from heterogeneous data sources. The primary challenge of ER lies in classifying record pairs as matches or nonmatches, which in multi-source ER (MS-ER)…
Large linear systems are ubiquitous in modern computational science and engineering. The main recipe for solving them is the use of Krylov subspace iterative methods with well-designed preconditioners. Recently, GNNs have been shown to be a…
The Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the…
Simulating gas flow within the divertor, which is a crucial component in nuclear fusion reactors, is essential for assessing and enhancing its design and performance. Traditional methods, such as the direct simulation Monte Carlo and the…
Tokamak design is inherently challenging due to several cross-competing effects which require a careful and calibrated treatment to obtain an optimal operational envelope. Incorporating physics across varied fidelities is crucial in this…
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…
In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes. The framework is composed…
Determining stress and strain in a component of a fusion power plant involves defining boundary conditions for the mechanical equilibrium equations, implying the availability of a full reactor model for defining those conditions. To address…
In this bachelor's thesis, isotope effects for pedestal instabilities have been studied based on an ASDEX Upgrade H-Mode scenario. This was done using the JOREK code for extended MHD simulations, including the ion diamagnetic drift and the…
This paper considers the numerical solution of Timoshenko beam network models, comprised of Timoshenko beam equations on each edge of the network, which are coupled at the nodes of the network using rigid joint conditions. Through…
Most linear algebra kernels in interior point methods for linear programming require the solution of linear systems of equation with the matrix $N = A^TD^{-1}A$ (or $AD^{-1}A^T$), where $A$ denotes the constraint matrix of the linear…
We introduce an extension to the AthenaK code for general-relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes using a 3+1 conservative Eulerian formulation. Like the fixed-spacetime GRMHD solver, we use standard finite-volume…
We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…
Solving the problem of fast eruptive events in magnetically dominated astrophysical plasmas requires the use of particularly well adapted numerical tools. Indeed, the central mechanism based on magnetic reconnection is determined by a…
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…
One of strengths in the finite element (FE) and Galerkin methods is their capability to apply weak formulations via integration by parts, which leads to elements matching at lower degree of continuity and relaxes requirements of choosing…