相关论文: Divergence-free Interpolation of Vector Fields Fro…
The paper aims at proposing an efficient and stable quasi-interpolation based method for numerically computing the Helmholtz-Hodge decomposition of a vector field. To this end, we first explicitly construct a matrix kernel in a general form…
In recent years, several different strategies have emerged for evolving the magnetic field in numerical MHD. Some of these methods can be classified as divergence-cleaning schemes, where one evolves the magnetic field components just like…
This paper presents an approach to enhance volume conservation in the immersed boundary (IB) method by using regularized delta functions derived from composite B-splines. The conventional IB method, while effective for fluid-structure…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
The magnetic field from a uniformly magnetised, rectangular prism is known exactly, which is the basis for a large number of micromagnetic simulations. Here we derive an analytical solution for the field from a periodically repeating…
Inferences of the magnetic field in the solar atmosphere by means of spectropolarimetric inversions (i.e., Stokes inversion codes) yield magnetic fields that are non-solenoidal($\nabla\cdot{\bf B} \ne 0$). Because of this, results obtained…
The nonlinear magnetic induction equation with Hall effect can be used to model magnetic fields, e.g. in astrophysical plasma environments. In order to give reliable results, numerical simulations should be carried out using effective and…
We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary…
The ideal Magnetohydrodynamics (MHD) equations are challenging because one needs to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Many numerical methods have been developed to enforce this condition. In this work, we…
This article introduces a new 3D magnetohydrodynamic (MHD) equilibrium solver, based on the concept of admissible variations of B, p that allows for magnetic relaxation of a magnetic field in a perturbed/non-minimum energy state to a lower…
We describe a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamics code based on the total variation diminishing scheme. Contributions from ambipolar diffusion terms…
We demonstrate vector magnetometry with an ensemble of nitrogen-vacancy (NV) centers in diamond without the need for an external bias field. The anisotropy of the electric dipole moments of the NV center reduces the ambiguity of the…
We modify an existing magnetohydrodynamics algorithm to make it more compatible with a dimensionally-split (DS) framework. It is based on the standard reconstruct-solve-average strategy (using a Riemann solver), and relies on constrained…
We present a new way to merge any two point distribution approaches using distance fields. Our new process allows us to produce digital stippling that fills areas with stipple dots without visual artifacts as well as includes clear linear…
The zero-bias conductance peak in d-wave superconductors splits in an applied magnetic field. In this work, the experimentally observed universal relation delta ~ B0^(1/2) for strip-shaped samples is derived analytically based on the…
We study hyperinterpolation and its spectral multiplier variants on the sphere under weak cubature assumptions formulated through Sobolev discrepancy estimates. In contrast with classical hyperinterpolation theory, our framework does not…
We present for astrophysical use a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference method on an Eulerian grid, called the Total Variation Diminishing…
The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning…
We present a constrained formulation of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for enforcing the \nabla\dot B = 0 constraint in Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we impose is…
Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants…