相关论文: On the performance of exponential integrators for …

Many Material Point Method implementations favor explicit time integration. However large time steps are often desirable for special reasons - for example, for partitioned coupling with another large-step solver, or for imposing…

The Lindblad equation is a widely used quantum master equation to model the dynamical evolution of open quantum systems whose states are described by density matrices. These solution matrices are characterized by semi-positiveness and trace…

A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…

We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…

As inverter-based resources (IBRs) penetrate power systems, the dynamics become more complex, exhibiting multiple timescales, including electromagnetic transient (EMT) dynamics of power electronic controllers and electromechanical dynamics…

Modern multi-core systems have a large number of design parameters, most of which are discrete-valued, and this number is likely to keep increasing as chip complexity rises. Further, the accurate evaluation of a potential design choice is…

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of…

This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…

New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulations are introduced. The new models include the variational…

We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of…

Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial…

In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…

A popular version of the finite strain Maxwell fluid is considered, which is based on the multiplicative decomposition of the deformation gradient tensor. The model combines Newtonian viscosity with hyperelasticity of Mooney-Rivlin type; it…

The goal of this paper is to develop energy-preserving variational integrators for time-dependent mechanical systems with forcing. We first present the Lagrange-d'Alembert principle in the extended Lagrangian mechanics framework and derive…

In certain astrophysical systems the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We…

The efficient numerical integration of large-scale matrix differential equations is a topical problem in numerical analysis and of great importance in many applications. Standard numerical methods applied to such problems require an unduly…

In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…

In this paper, we propose and analyse a novel class of exponential collocation methods for solving conservative or dissipative systems based on exponential integrators and collocation methods. It is shown that these novel methods can be of…

Multiderivative time integrators have a long history of development for ordinary differential equations, and yet to date, only a small subset of these methods have been explored as a tool for solving partial differential equations (PDEs).…

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT), and thereby furnish a more accurate and reliable description of the electronic structure in…