Related papers: Divergence-free Interpolation of Vector Fields Fro…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
Many phenomena in the Sun's atmosphere are magnetic in nature and study of the atmospheric magnetic field plays an important part in understanding these phenomena. Tools to study solar magnetic fields include magnetic topology and features…
Preserving the admissible set of the ideal magnetohydrodynamics (MHD) equations is important not only for producing physically meaningful numerical solutions, but more importantly for achieving robust computations. In this paper, we develop…
We present an analysis of data stemming from numerical simulations of decaying magnetohydrodynamic (MHD) turbulence up to grid resolution of 1536^3 points and up to Taylor Reynolds number of 1200. The initial conditions are such that the…
We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
We introduce a novel type of approximation spaces for functions with values in a nonlinear manifold. The discrete functions are constructed by piecewise polynomial interpolation in a Euclidean embedding space, and then projecting pointwise…
Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
We study a general convergence theory for the numerical solutions of compressible viscous and electrically conducting fluids with a focus on numerical schemes that preserve the divergence free property of magnetic field exactly. Our…
Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing…
We report a new finite-difference scheme for two-dimensional magnetohydrodynamics (MHD) simulations, with and without rotation, in unstructured grids with quadrilateral cells. The new scheme is implemented within the code VULCAN/2D, which…
We describe a new algorithm \texttt{Miranda} for isolating the simple zeros of a function $\boldsymbol{f}:{\mathbb R}^n\to{\mathbb R}^n$ within a box $B_0\subseteq {\mathbb R}^n$. The function $\boldsymbol{f}$ and its partial derivatives…
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an…
Accurate measurement of vector magnetic fields is critical for applications including navigation, geoscience, and space exploration. Nitrogen-vacancy (NV) center spin ensembles offer a promising solution for high-sensitivity vector…
We apply topological methods to better understand how the magnetic field in the stellarator edge can be diverted away from the confined region. Our primary method is calculating the winding numbers of closed contours, which gives…
This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. Boundary conditions are…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
This paper extends previous work on finitedifference schemes over staggered grids for infinite-dimensional port-Hamiltonian systems. In the one-dimensional setting, it generalizes the discretization approach originally developed for the…