Related papers: A high-performance elliptic solver for plasma boun…
We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved…
We present the IAMReX, an adaptive and parallel solver for particle-resolved simulations on the multi-level grid. The fluid equations are solved using a finite-volume scheme on the block-structured semi-staggered grids with both subcycling…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
We present a matrix-free GPU multigrid preconditioner with algebraically consistent coarsening for solving Poisson equations on adaptive octree grids with irregular domains. Within uniform-resolution regions, the coarsening satisfies the…
We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal…
We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz…
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…
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces. Since the solution has low regularity across…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
Turbulent dynamics in the scrape-off layer (SOL) of magnetic fusion devices is intermittent with large fluctuations in density and pressure. Therefore, a model is required that allows perturbations of similar or even larger magnitude to the…
A novel and scalable geometric multi-level algorithm is presented for the numerical solution of elliptic partial differential equations, specially designed to run with high occupancy of streaming processors inside Graphics Processing…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with…
We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two…
A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic…
Numerical climate- and weather-prediction requires the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous properties. They can be used for arbitrary domains and support a…
In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the elliptic equation with homogeneous…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…