Related papers: Magnetic Field Simulations Using Explicit Time Int…
We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects…
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of…
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…
We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen--Cahn equation as an example: one fully implicit nonlinear method and one semi-implicit linear method.…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable accuracy and stability problems, they give rise to large and complicated systems of…
This paper proposes a decoupled numerical scheme of the time-dependent Ginzburg--Landau equations under the temporal gauge. For the magnetic potential and the order parameter, the discrete scheme adopts the second type Ned${\rm…
This work presents a high-order isogeometric formulation for magnetoquasistatic eddy-current problems based on a decomposition into Biot-Savart-driven source fields and finite-element reaction fields. Building upon a recently proposed…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
The finite-element analysis of three-dimensional magnetostatic problems in terms of magnetic vector potential has proven to be one of the most efficient tools capable of providing the excellent quality results but becoming computationally…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
A fast and stable numerical method is formulated to compute the time evolution of a wave function in a magnetic field by solving the time-dependent Schroedinger equation. This computational method is based on the finite element method in…
In this work, an approximate family of implicit multiderivative Runge-Kutta (MDRK) time integrators for stiff initial value problems is presented. The approximation procedure is based on the recent Approximate Implicit Taylor method (Baeza…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
Using an explicit Euler substitution it was obtained a system of differential equations, which can be used to find the solution of time-dependent 1-dimentional Schr\H{o}dinger equation for a general form of the time-dependent potential.
We propose an arbitrarily higher (even) order implicit leapfrog scheme for time discretization of a three-field formulation of Maxwell's equations. We use this in conjunction with an arbitrarily higher-order and compatible discretization…
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).…