Related papers: Systems of Differential Algebraic Equations in Com…
Despite of the topical engineering need and all scientific investments, the mathematical formulation of modeling elastic deformations in magnetic systems is not yet fully established. Often, especially in electrical engineering…
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear…
We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
Electromagnetic quasistatic (EMQS) fields, where radiation effects are neglected, while Ohmic losses and electric and magnetic field energies are considered, can be modeled using Darwin-type field models as an approximation to the full…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation.…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. Tey are reviewed in the work presented. It is drawing the attention on the following aspects. EM-field has in general case quaternion…
We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is then applied to the Schr\"{o}dinger equation in…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are…
A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the…
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…