相关论文: Magnus integrators on multicore CPUs and GPUs

We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…

The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs…

We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…

The present research builds on a recently proposed spatial prediction method for discretized two-dimensional data, based on a suitably modified planar rotator (MPR) spin model from statistical physics. This approach maps the measured data…

This paper presents a matrix-free multigrid method for solving the Stokes problem, discretized using $H^{\text{div}}$-conforming discontinuous Galerkin methods. We employ a Schur complement method combined with the fast diagonalization…

The ever-growing size of modern space-time data sets, such as those collected by remote sensing, requires new techniques for their efficient and automated processing, including gap-filling of missing values. CUDA-based parallelization on…

This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…

We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…

This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…

Emerging analog computing substrates, such as oscillator-based Ising machines, offer rapid convergence times for combinatorial optimization but often suffer from limited scalability due to physical implementation constraints. To tackle…

In this paper, we show how the It\^o-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To this end, we will first discretize the SPDE in space…

Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…

It is often the case that, while the numerical solution of the non-linear dispersive equation $\mathrm{i}\partial_t u(t)=\mathcal{H}(u(t),t)u(t)$ represents a formidable challenge, it is fairly easy and cheap to solve closely related linear…

In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…

We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…

We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schr\"odinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes…

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central…

We report numerical results on solving constrained linear-quadratic model predictive control (MPC) problems by exploiting graphics processing units (GPUs). The presented method reduces the MPC problem by eliminating the state variables and…