Related papers: Solving the Vlasov equation for one-dimensional mo…
In this paper, we describe our approach to develop a simulation software application for the fully kinetic Vlasov equation which will be used to explore physics beyond the gyrokinetic model. Simulating the fully kinetic Vlasov equation…
This paper gives an analysis and an evaluation of linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetics with double precision. Knowing the performance of these operations, iterative Krylov methods are…
The self-join finds all objects in a dataset that are within a search distance, epsilon, of each other; therefore, the self-join is a building block of many algorithms. We advance a GPU-accelerated self-join algorithm targeted towards high…
This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and…
We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…
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…
As a first approximation beyond linearity, the nonlinear Schr\"odinger equation (NLSE) reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally…
In this paper, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic…
Particle-based simulations of the Vlasov equation typically require a large number of particles, which leads to a high-dimensional system of ordinary differential equations. Solving such systems is computationally very expensive, especially…
The linearized Vlasov equation for a plasma system in a uniform magnetic field and the corresponding linear Vlasov operator are studied. The spectrum and the corresponding eigenfunctions of the Vlasov operator are found. The spectrum of…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…
In this study, the Vlasov-Poisson equation with or without collision term for plasma is solved by the unified gas kinetic scheme (UGKS). The Vlasov equation is a differential equation describing time evolution of the distribution function…
In this paper we present new versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in two and three spatial dimensions in imaginary and in real time,…
We present a new numerical scheme for solving the advection equation and its application to the Vlasov simulation. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…
Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating…
Parallel algorithms on CPU and GPU are implemented for the Unified Gas-Kinetic Scheme and their performances are investigated and compared by a two dimensional channel flow case. The parallel CPU algorithm has a one dimensional block…
An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled,…
This paper is devoted to consideration of the theory of collisionless statistical systems with interparticle scalar interaction. The mathematical model of such systems is constructed and the exact solution of Vlasov equation for isotropic…
Existing approaches to solving the Vlasov equation treat the system as a partial differential equation on a phase space grid, and track in either an Eulerian, Lagrangian, or semi-Lagrangian picture. We present an alternative approach, which…