Related papers: Discretization anisotropy in micromagnetic simulat…
We use a numerical electromagnetic simulation software to investigate a filtering device consisting of a small dimensional microstrips embedded with a thin layer of ferromagnetic material and we compare our results to experimental results.…
Numerical integration of a stochastic Landau-Lifshitz-Gilbert equation is used to study dynamic processes in single-domain nanoscale magnets at nonzero temperatures. Special attention is given to including thermal fluctuations as a Langevin…
We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which…
The Landau-Lifshitz equation governing magnetization dynamics is written in terms of the amplitudes of normal modes associated with the micromagnetic system's appropriate ground state. This results in a system of nonlinear ordinary…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…
Many materials such as martensitic or ferromagnetic crystals are observed to be in metastable states exhibiting a fine-scale, structured spatial oscillation called microstructure; and hysteresis is observed as the temperature, boundary…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
This paper investigates the discretization of a periodic metasurface and demonstrates how such a surface can achieve perfect anomalous reflection. Whilst most contemporary theoretical works on metasurfaces deal with continuous current or…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
For three-dimensional (3D) magnetic objects with linear size $L$ exceeding a few exchange lengths, the micromagnetic state exhibits pronounced informational sparsity: low-dimensional, high-gradient regions (e.g., domain walls) coexist with…
A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
Designing well-defined magnetic nanomaterials is crucial for various applications and it demands a comprehensive understanding of their magnetic properties at the microscopic level. In this study, we investigate the contributions to the…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Anisotropic barostats are employed to carry out Molecular Dynamics simulations where the volume is allowed to fluctuate with no constraints on the shape of the simulation cell. Most of these algorithms are based on second-order differential…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
This paper presents the state of the art of kinetic modeling techniques for simulating plasma kinetic dynamics in magnetospheres. We describe the critical numerical techniques for enabling large-scale kinetic simulations of magnetospheres:…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
This article presents a new numerical scheme for the discretization of dissipative particle dynamics with conserved energy. The key idea is to reduce elementary pairwise stochastic dynamics (either fluctuation/dissipation or thermal…