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The laws of physics may often be transformed mathematically into second-order partial differential equations (PDEs). Few of these equations have exact solutions, however, which explains why they do not receive the attention they deserve in the academic curriculum.

The main purpose of this book is to exploit the free Lite Version of FlexPDE for solving PDEs occurring in physics. It solves a typical example in seconds and promptly presents the results graphically by a variety of plots.

This book begins by presenting the graphical facilities available and solving some simple Laplace and Poisson equations. The main part of the volume is devoted to applications (in 2D and 3D) to electriciy and magnetism, heat transport, electromagnetic waves, wave mechanics and viscous flow.

The volume comprises 125 examples, illustrated by plots, and there are also end-of-chapter exercises.
Script modifications will need to be made to run with current version.
Scripts used in this volume are available here.

The book begins by explaining the plotting facilities of FlexPDE by simple examples. After an introduction to Laplace and Poisson equations it shows how the definitions of strain, Hooke's law, and the relations of force balance lead to 2^nd-order partial differential equations, which may be solved conveniently by the Free Lite Version of FlexPDE.

The first elasticity applications are elementary, but the following chapters involve an analysis of principal axes and the corresponding strains and stresses. The static analysis includes torsion, warping, and thermoelastic deformation. Forces, bending moments and energy are also obtained.

The dynamic analysis follows the same general pattern as the static counterpart, with the difference that the equations of equilibrium are replaced by Newton's law of motion. There are also chapters on resonant vibration, eigenvalues and eigenstates in both 2D and 3D.

The volume comprises 95 examples, illustrated by plots, and there are also end-of-chapter exercises.
Script modifications will need to be made to run with current version.
Scripts used in this volume are available here.

This book summarizes, defines, and contextualizes multiphysics with an emphasis on porous materials. It covers various essential aspects of multiphysics, from history, definition, and scope to mathematical theories, physical mechanisms, and numerical implementations. The emphasis on porous materials maximizes readers’ understanding as these substances are abundant in nature and a common breeding ground of multiphysical phenomena, especially complicated multiphysics. Dr. Liu’s lucid and easy-to-follow presentation serve as a blueprint on the use of multiphysics as a leading edge technique for computer modeling. The contents are organized to facilitate the transition from familiar, monolithic physics such as heat transfer and pore water movement to state-of-the-art applications involving multiphysics, including poroelasticity, thermohydro-mechanical processes, electrokinetics, electromagnetics, fluid dynamics, fluid structure interaction, and electromagnetomechanics. This volume serves as both a general reference and specific treatise for various scientific and engineering disciplines involving multiphysics simulation and porous materials.

• Presents the essential components of multiphysics along with innovative numerical modeling techniques in the context of porous materials
• Structured for a wide range of readers from those new to the field to experts, instructors, researchers, software developers, and modelers from many scientific and engineering disciplines
• Organized using a practical approach that combines a logical presentation of theories with illustrative hands-on example problems
• Reinforces multiphysics concepts with applications demonstrating the use of common software to solve representative problems

This book is available for purchase in electronic form at Springer

This material is also discussed on Dr. Liu's website at www.multiphysics.us

Electrostatic problem solving in two and three dimensions is explained using FlexPDE. It is written for advanced students who have had courses in basic electrostatics.

The goal of this book is to enable students to use finite elements to solve many of the problems of electromagnetic field theory that cannot be solved analytically by advanced mathematical analysis.

Being able to quickly get solutions to new problems, make changes in them and view the results graphically leads more rapidly to physical understanding than spending hours working with complex mathematics.

This book is available for purchase in electronic form at GooglePlay and other online sources.
 

FlexPDE usage for the modeling of image processing (Edge Detection, Diffusion Smoothing, and Wavelet Transform) via methods of Mathematical Physics. All topics are supplied with the examples and exercises for FlexPDE 5 free Lite Version.
Script modifications will need to be made to run with current version.

This e-book (in Russian) is available for purchase at GRIN Verlag.
(The GRIN Verlag site is in German, but English and French are available in the upper right corner of the site.)