Related papers: Time evolution of nanoscale systems by finite diff…
We present a novel fully fourth order in time and space {finite difference method for the time domain Maxwell's equations} in metamaterials. We consider a Drude metamaterial model for the material response to incident electromagnetic…
A space-time fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes,…
The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo's time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can…
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential…
Irksome is a library based on the Unified Form Language (UFL) that automates the application of Runge-Kutta time-stepping methods for finite element spatial discretizations of partial differential equations (PDEs). This paper describes…
The discrete autonomous/non-autonomous Toda equations and the discrete Lotka-Volterra system are important integrable discrete systems in fields such as mathematical physics, mathematical biology and statistical physics. They also have…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed…
The purpose of this work is to test the application of the finite element method to quantum mechanical problems, in particular for solving the Schroedinger equation. We begin with an overview of quantum mechanics, and standard numerical…
A linear evolving surface partial differential equation is first discretized in space by an arbitrary Lagrangian Eulerian (ALE) evolving surface finite element method, and then in time either by a Runge-Kutta method, or by a backward…
Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…
A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled non-linear differential equations. A first integral of this set is analytically obtained. The time evolution of the…
Time discretizations of phase-field systems have been studied. For example, a time discretization and an error estimate for a parabolic-parabolic phase-field system have been studied by Colli--K. [Commun. Pure Appl. Anal. 18 (2019)]. Also,…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
The goal of this work is to analyze a model for the rate-independent evolution of sets with finite perimeter. The evolution of the admissible sets is driven by that of a given time-dependent set, which has to include the admissible sets and…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
The paper introduces a finite element method for an Eulerian formulation of partial differential equations governing the transport and diffusion of a scalar quantity in a time-dependent domain. The method follows the idea from Lehrenfeld &…