Related papers: Obtaining Potential Field Solution with Spherical …
Magnetic fields are one of the most important drivers of the highly dynamic processes that occur in the lower solar atmosphere. They span a broad range of sizes, from large- and intermediate-scale structures such as sunspots, pores and…
In this paper, we will use the interior functions of an hierarchical basis for high order $BDM_p$ elements to enforce the divergence-free condition of a magnetic field $B$ approximated by the H(div) $BDM_p$ basis. The resulting constrained…
Numerical reconstruction/extrapolation of coronal nonlinear force-free magnetic field (NLFFF) usually takes the photospheric vector magnetogram as input at the bottom boundary. Magnetic field observed at the photosphere, however, contains…
Investigating the solar magnetic field is crucial to understand the physical processes in the solar interior as well as their effects on the interplanetary environment. We introduce a novel method to predict the evolution of the solar…
With the use of the general covariant matrix 10-dimensional Petiau-Duffin-Kemmer formalism in cylindrical coordinates exact solutions of the quantum-mechanical equation for a particle with spin 1 in the presence of an external homogeneous…
In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding…
A hybrid spectral/finite-element code is developed to numerically solve the resistive finite-pressure magnetohydrodynamic equilibria without the necessity of postulating nested magnetic flux surfaces in the non-axisymmetric toroidal…
Fundamental bounds on quadratic electromagnetic metrics are formulated and solved via convex optimization. Both dual formulation and method-of-moments formulation of the electric field integral equation are used as key ingredients. The…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. The field calculations can be improved by…
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are…
We compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a…
The standard design method for conventional straight dipole magnets is improved in this paper. The good field region is not symmetric with respect to the magnet mechanical center, and its width is not enlarged to include the beam sagitta.…
This article describes a method devised for efficient evaluation of arbitrary static magnetic and electric fields in a source free region needed for long time tracking of charged particles. Field values given on the boundary of the region…
Spectropolarimetric reconstructions of the photospheric vector magnetic field are intrinsically limited by the 180$^\circ$-ambiguity in the orientation of the transverse component. So far, the removal of such an ambiguity has required…
In this paper we propose an approach of obtaining of N-dimensional spherical harmonics based exclusively on the methods of solutions of differential equations and the use of the special functions properties. We deduce the Laplace-Beltrami…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of…
We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific…