The Cell Method: A Purely Algebraic Computational Method in Physics and Engineering

The Cell Method (CM) is a computational tool that maintains critical
multidimensional attributes of physical phenomena in analysis. This
information is neglected in the differential formulations of the classical
approaches of finite element, boundary element, finite volume,
and finite difference analysis, often leading to numerical instabilities
and spurious results.
This book highlights the central theoretical concepts of the CM that
preserve a more accurate and precise representation of the geometric
and topological features of variables for practical problem solving.
Important applications occur in fields such as electromagnetics, electrodynamics,
solid mechanics and fluids. CM addresses non-locality
in continuum mechanics, an especially important circumstance in
modeling heterogeneous materials. Professional engineers and scientists,
as well as graduate students, are offered:
• A general overview of physics and its mathematical descriptions;
• Guidance on how to build direct, discrete formulations;
• Coverage of the governing equations of the CM, including nonlocality;
• Explanations of the use of Tonti diagrams; and
• References for further reading.