Related papers: An integral equation-based numerical solver for Ta…
Context. The understanding of fossil fields origin, topology and stability is one of the corner stones of the stellar magnetism theory. On one hand, since they survive over secular time-scales, they may modify the structure and the…
Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a…
We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$…
This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
We present a generic technique, automated by computer-algebra systems and available as open-source software \cite{scuff-em}, for efficient numerical evaluation of a large family of singular and nonsingular 4-dimensional integrals over…
Inspired by G. Frieden's recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct a novel family of discrete integrable systems which can be regarded…
An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can…
We develop a numerical solver, that extends the computational framework considered in [Phys. Rev. D 65, 084016 (2002)], to include scalar perturbations of nonrotating black holes. The nonlinear Einstein-Klein-Gordon equations for a massless…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
We present a new numerical model for solving the Chew-Goldberger-Low system of equations describing a bi-Maxwellian plasma in a magnetic field. Heliospheric and geospace environments are often observed to be in an anisotropic state with…
Simulating electromagnetic fields across broad frequency ranges is challenging due to numerical instabilities at low frequencies. This work extends a stabilized two-step formulation of Maxwell's equations to the time-domain. Using a…
An essentially unique homeomorphic solution to the Beltrami equation was found in the 1960s using the theory of Calder\'{o}n-Zygmund and singular integral operators in $L^p(\mathbb C)$. We will present an alternative method to solve the…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
Spherically symmetric static topological black hole solutions associated with some extended higher order gravitational models in the presence of a Maxwell-field are derived by means of simple Lagrangian method, based on spherically…
The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are…
We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…
We investigate the representations of the solutions to Maxwell's equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. Our approach provides us with a characterization for the…
The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into…
The Robinson-Trautman solution in the Einstein-Maxwell-$\Lambda$ system admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. Restricting to the case where the Maxwell field is aligned, i.e., the…