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Artificial square spin ices are structures composed of magnetic elements arranged on a geometrically frustrated lattice and located on the sites of a two-dimensional square lattice, such that there are four interacting magnetic elements at…
Cartesian-grid methods in combination with immersed-body and volume-of-fluid methods are ideally suited for simulating breaking waves around ships. A surface panelization of the ship hull is used as input to impose body-boundary conditions…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
The automated finite element analysis of complex CAD models using boundary-fitted meshes is rife with difficulties. Immersed finite element methods are intrinsically more robust but usually less accurate. In this work, we introduce an…
Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, including many in continuum mechanics, possess a wide variety of space-time scales; often they possess a continuum of space-time…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
This note describes the full approximation storage (FAS) multigrid scheme for an easy one-dimensional nonlinear boundary value problem. The problem is discretized by a simple finite element (FE) scheme. We apply both FAS V-cycles and…
We investigate the formation and early evolution and fragmentation of an accretion disk around a forming massive protostar. We use a grid-based self-gravity-radiation-hydrodynamics code including a sub-grid module for stellar and dust…
The dispersed node locations and complex topologies of edge networks, combined with intricate dynamic microservice dependencies, render traditional centralized microservice architectures (MSAs) unsuitable. In this paper, we propose a…
A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to…
A grid-overlay finite difference method is proposed for the numerical approximation of the fractional Laplacian on arbitrary bounded domains. The method uses an unstructured simplicial mesh and an overlay uniform grid for the underlying…
Frustrated spin-ice systems support emergent gauge fields and fractionalized quasiparticles that act as magnetic monopoles. Although artificial platforms have enabled their direct visualization, access to their quantum-coherent dynamics has…
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns…
Anomalous radio flux ratios in four-image gravitational lens systems can be explained by adding a clumpy cold dark matter (CDM) component to the potential of the lens galaxy. Evans & Witt (2003) recently suggested that smooth multipole…
The stellar disc kinematics in a sample of fifteen intermediate- to late-type edge-on spiral galaxies are studied using a dynamical modeling technique. The sample covers a substantial range in maximum rotation velocity and deprojected…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
This article is concerned with the internal dynamics of a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res., 95, D2 (1990) 1955-1963] to explain central features of the glacial cycles observed in the climate record of the…
The physical processes taking place at the edge region are crucial for the operation of tokamaks as they govern the interaction of hot plasma with the vessel walls. Numerical modeling of the edge with state-of-the-art codes attempts to…