Related papers: Explicit Exponential Rosenbrock Methods and their …
The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…
The efficient numerical solution of many kinetic models in plasma physics is impeded by the stiffness of these systems. Exponential integrators are attractive in this context as they remove the CFL condition induced by the linear part of…
Timed model checking has been extensively researched in recent years. Many new formalisms with time extensions and tools based on them have been presented. On the other hand, Explicit-Time Description Methods aim to verify real-time systems…
We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as…
We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation…
A fundamental task in particle-in-cell (PIC) simulations of plasma physics is solving for charged particle motion in electromagnetic fields. This problem is especially challenging when the plasma is strongly magnetized due to numerical…
We change a previous time-stepping algorithm for solving a multi-scale Vlasov-Poisson system within a Particle-In-Cell method, in order to do accurate long time simulations. As an exponential integrator, the new scheme allows to use large…
Application for semantic segmentation models in areas such as autonomous vehicles and human computer interaction require real-time predictive capabilities. The challenges of addressing real-time application is amplified by the need to…
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact…
In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based…
This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
The structural flexibility of the exponential propagation iterative methods of Runge-Kutta type (EPIRK) enables construction of particularly efficient exponential time integrators. While the EPIRK methods have been shown to perform well on…
Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…
Simulations of many rigid bodies colliding with each other sometimes yield particularly interesting results if the colliding objects differ significantly in size and are non-spherical. The most expensive part within such a simulation code…
Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS…
EXPODE is a MATLAB toolbox for exponential time integration. It supports exponential Runge-Kutta- and Rosenbrock-methods, linearized and non-linearized multistep-methods and the EXP4. We support evaluation of the arising matrix functions…
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…
Convexity splitting like schemes with improved accuracy are proposed for a phase field model for surface diffusion. The schemes are developed to enable large scale simulations in three spatial dimensions describing experimentally observed…
A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially…