This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our
approach is to develop DEC using only discrete combinatorial and geometric operations on …

We present a theory and applications of discrete exterior calculus on simplicial complexes of
arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory …

Why do we have analogies in physics? This question has been the leitmotif of the author's
research for about half a century. Six physical theories are considered: particle mechanics …

A new discontinuous Galerkin spectral element time-domain (DG-SETD) method for
Maxwell's equations based on the field variables E and B is proposed to analyze three …

Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using
geometric and symmetry techniques. Computational algorithms obtained from a discrete …

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 …

This paper presents a modified thermal model-based double-loop circulatory technique for
the thermal analyses of permanent magnet synchronous machines. The inner loop of the …

The purpose of this note… is to sort out my own thoughts… and to solicit ideas from others.
Lloyd N. Trefethen Three mysteries of Gaussian elimination Since 2008, when the first …

Abstract A new Discontinuous Galerkin Time Domain (DGTD) method for solving the 3D time
dependent Maxwell's equations via the electric field intensity E and magnetic flux density B …

Solutions of many physical problems have salient local features that are qualitatively known
a priori (for example, singularities at point sources, edge and corners; boundary layers; …