Related papers: Second-order semi-implicit projection methods for …
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…
The second moment method is a linear acceleration technique which couples the transport equation to a diffusion equation with transport-dependent additive closures. The resulting low-order diffusion equation can be discretized independent…
We present and investigate a new type of implicit fractional linear multistep method of order two for fractional initial value problems. The method is obtained from the second order super convergence of the Gr\"unwald-Letnikov approximation…
Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…
A method for time-reversible numerical integration of the deterministic Landau-Lifshitz Gilbert equation by means of a second order Suzuki-Trotter decomposition is presented and tested against commonly used second order predictor-corrector…
We derive a variational formulation for thin film magnetization problems in type-II superconductors written in terms of two variables, the electric field and the magnetization function. A numerical method, based on this formulation, makes…
Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and [Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau-Lifshitz-Gilbert (LLG)…
The Landau-Lifshitz (L-L) equation describing the time dependence of the magnetisation vector is numerically integrated fully without any simplifying assumptions in the time domain and the magnetisation time series obtained is Fourier…
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…
The Landau--Lifshitz--Baryakhtar (LLBar) and the Landau--Lifshitz--Bloch (LLBloch) equations are nonlinear vector-valued PDEs which arise in the theory of micromagnetics to describe the dynamics of magnetic spin field in a ferromagnet at…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of space-time fractional advection-diffusion equations. To start with, an implicit method based on two-sided Gr\"unwald formulae is…
This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely, we consider an implicit-explicit Crank-Nicolson scheme as…
Laser-induced magnetization precession measurements in ferromagnets often reveal an anomalous decrease in the damping time near a field-induced second-order spin-orientation transition, a behavior that cannot be described by the linearized…
Dynamic simulations of spin-transfer and spin-orbit torques are increasingly important for a wide range of spintronic devices including magnetic random access memory, spin-torque nano-oscillators and electrical switching of…
This paper proposes a strong second-order two-step explicit/implicit technique with spectral orthogonal basis Galerkin finite element method for solving a two-dimensional Gray-Scott model subject to appropriate initial and boundary…
In this paper, based on inertial and Tseng's ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the…
A new methodology for micromagnetic simulations of magnetic nanocomposites is presented. The methodology is especially suitable for simulations of two-phase composites consisting of magnetically hard inclusions in a soft magnetic matrix…
We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…
Imposition methods of interface conditions for the second-order wave equation with non-conforming grids is considered. The spatial discretization is based on high order finite differences with summation-by-parts properties. Previously…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…