Related papers: Fast solvers for Tokamak fluid models with PETSC
We present the verification, validation, and results of an approximate, analytic model for the radial profile of the stress, strain, and displacement within the toroidal field (TF) coil of a Tokamak at the inner midplane, where stress…
In this work we construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a…
This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase…
Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…
At the heart of the Met Office climate and weather forecasting capabilities lies a sophisticated numerical model which solves the equations of large-scale atmospheric flow. Since this model uses semi-implicit time-stepping, it requires the…
We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduction of an HDG flux of the dual saddle-point form of the MHD…
The Brinkman equations can be regarded as a combination of the Stokes and Darcy equations which model transitions between the fast flow in channels (governed by Stokes equations) and the slow flow in porous media (governed by Darcy's law).…
The design of commercially feasible magnetic confinement fusion reactors strongly relies on the reduced turbulent transport in the plasma edge during operation in the high confinement mode (H-mode). We present first global turbulence…
We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
Simulations at physical quark masses are affected by the critical slowing down of the solvers. Multigrid preconditioning has proved to deal effectively with this problem. Multigrid accelerated simulations at the physical value of the pion…
We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfv\'en eigenmodes and energetic particle transport in tokamak plasmas. In order…
In this paper we present a novel pressure-based semi-implicit finite volume solver for the equations of compressible ideal, viscous and resistive magnetohydrodynamics (MHD). The new method is conservative for mass, momentum and total energy…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…
We present in this paper a hybrid, Multi-Level Monte Carlo (MLMC) method for solving the neutral particle transport equation. MLMC methods, originally developed to solve parametric integration problems, work by using a cheap, low fidelity…
Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
In the present study, we establish two new block variants of the Conjugate Orthogonal Conjugate Gradient (COCG) and the Conjugate A-Orthogonal Conjugate Residual (COCR) Krylov subspace methods for solving complex symmetric linear systems…
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…