This survey paper describes recent developments in the area of parametrized variational
principles (PVPs) and selected applications to finite-element computational mechanics. A …

This is a textbook written for use in a graduate-level course for students of mechanics and
engineering science. It is designed to cover the essential features of modern variational …

Motivated by practical problems in engineering and physics, drawing on a wide range of
applied mathematical disciplines, this book is the first to provide, within a unified framework …

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 …

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 …

This chapter presents a comprehensive review and some new developments on canonical
duality theory for nonconvex systems. Based on a tricanonical form for quadratic …

It is shown that for every linear or nonlinear problem, whose solution exists and is unique,
one may find many functionals whose minimum is the solution of the problem. They are …

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 …

Dual minimum principles for displacements and stresses are well established for linear
variational problems and also for nonlinear (and monotone) constitutive laws. This paper …

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 …