Unified boundary integral equation and unified boundary element equation

Using functional analysis, a generalized operator equation is devised to describe almost all the boundary-value problems of various physical disciplines such as electrodynamics, solid mechanics, fluid mechanics, thermodynamics, etc. From the generalized operator equation, a unique unified boundary integral equation is developed which represents almost all the boundary integral equations of these various physical discipline. From the unified boundary integral equation, by discretization, follows a unique boundary-element equation which represents almost all the boundary-element equations of the various physical disciplines. A number of practical examples in electrodynamics, solid mechanics, fluid mechanics, and thermodynamics are worked out in detail to illustrate this powerful tool of the unified theory, which can be used to study various disciplines by the BEM (boundary-element method) systematically and to develop a BEM expert system