Related papers: A second-order numerical method for Landau-Lifshit…
We propose an efficient numerical method to obtain local order parameter in two-dimensional systems using spiral boundary conditions. As a benchmark, we first estimate the magnitude of staggered magnetization for the $S=1/2$ XXZ Heisenberg…
We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…
This paper considers the extreme type-II Ginzburg-Landau equations, a nonlinear PDE model that describes the states of a wide range of superconductors. For two-dimensional grids, a robust method is developed that performs a numerical…
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing…
The micropolar Rayleigh-B{\'e}nard convection system, which consists of Navier-Stokes equations, the angular momentum equation, and the heat equation, is a strongly nonlinear, coupled, and saddle point structural multiphysics system. A…
We discuss a mass-lumped midpoint scheme for the numerical approximation of the Landau-Lifshitz-Gilbert equation, which models the dynamics of the magnetization in ferromagnetic materials. In addition to the classical micromagnetic field…
We consider a multiscale strategy addressing the disparate scales in the Landau-Lifschitz equations in micro-magnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic…
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
A global approximation method of Nystr\"om type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first…
This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…
This paper investigates the time-optimal control problem for the Landau-Lifshitz-Bloch (LLB) equation, a macroscopic model that characterizes magnetization dynamics in ferromagnetic materials across a wide temperature range, including near…
The Landau potential in the general Ginzburg-Landau theory with two order parameters and all possible quadratic and quartic terms cannot be minimized with the straightforward algebra. Here, a geometric approach is presented that circumvents…
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…
A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees for each local element. Convergence of both…
Spin currents act on ferromagnets by exerting a torque on the magnetisation. This torque is modelled by appending additional terms to the Landau-Lifshitz-Gilbert equation motivating the study of the non-homogeneous Landau-Lifshitz-Gilbert…
A simplified model is introduced and analysed to show, that for the Landau-Lifshitz equation stable, steady state solutions of domain type exist in ferromagnetic systems, strongly driven by external transverse fields. These dynamic domain…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
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…
An efficient method for computing thermodynamic equilibrium states at the micromagnetic length scale is introduced, using the Markov chain Monte Carlo method. Trial moves include not only rotations of vectors, but also a change in their…