A general methodology for the solution of partial differential equations is described in which
the discretization of the calculus is exact and all approximation occurs as an interpolation …

We develop and present high-order mixed finite-element discretizations of the time-
dependent electromagnetic diffusion equations for solving eddy-current problems on three …

Compatible or mimetic numerical methods typically use vector components as the primary
unknowns in the discretization. It is frequently necessary or useful to be able to recover …

Recently a new class of biocompatible elastic polymers loaded with small ferrous particles, a
magnetoelastic polymer, has been developed. This engineered material is formed into a thin …

We present the development and application of compatible finite element discretizations of
electromagnetics problems derived from the time dependent, full wave Maxwell equations …

Differential forms are often presented to mathematicians as the underpinning of modern
calculus. The dx familiar to calculus students, for example, is revealed to be the most basic …

The goal of this dissertation is twofold. The first part concerns the development of a
numerical method for solving Maxwell's equations on unstructured hexahedral grids that …

The discretization of transient and static magnetic field problems with the Whitney Finite
Element Method results in differential-algebraic systems of equations of index 1 and …

Purpose–A family of preconditioned dual‐primal FETI iterative algorithms for the solution of
algebraic systems arising from edge element approximations in two dimensions is …

This thesis studies the approximation of solutions to partial differential equations (PDEs)
over domains discretized by the dual of a simplicial mesh. While primal'methods associate …