We present a new numerical method for the solution of field equations. The essence of the
method is to directly provide a discrete formulation of field laws, without using and requiring …

The objective of this paper is to present an approach to electromagnetic field simulation
based on the systematic use of the global (ie integral) quantities. In this approach, the …

In this paper, some structures which underlie the numerical treatment of second-order
boundary value problems are studied using magnetostatics as an example. The authors …

We show that the equations of electromagnetism can be directly obtained in a finite form, ie,
discrete, thus avoiding the traditional discretization methods of Maxwell's differential …

We propose an analysis (discretization techniques, convergence) of numerical schemes for
Maxwell equations which use two meshes (not necessarily tetrahedral), dual to each other …

Publisher Summary This chapter presents a set of conceptual tools for the formulation of
physical field problems in discrete terms. These tools allow the representation of the …

The geometrical approach to Maxwell's equations promotes a way to discretize them that
can be dubbed “Generalized Finite Differences”, which has been realized independently in …

By exploiting the geometric structure behind Maxwell's equations, the so called discrete
geometric approach allows to translate the physical laws of electromagnetism into discrete …

We examine the construction of a symmetric positive definite conductance matrix for eddy-
current problems, using a discrete approach. We construct a new set of piecewise uniform …

Using a geometric formulation for eddy currents, we present a geometric approach to
constructing approximations of the discrete magnetic and Ohm's constitutive matrices. In the …