Analytic Element Method across Fields of Study

2020 ◽  
pp. 1-70
Author(s):  
David R. Steward
Keyword(s):  
Philosophical Perspective ◽  
Analytic Element Method ◽  
Analytic Element ◽  
Fields Of Study ◽  
Wide Range ◽  
Analytic Elements ◽  
Element Method

This chapter introduces the philosophical perspective for solving problems with the Analytic Element Method, organized within three common types of problems: gradient driven flow and conduction, waves, and deformation by forces. These problems are illustrated by classic, well known solutions to problems with a single isolated element, along with their extension to complicated interactions occurring amongst collections of elements. Analytic elements are presented within fields of study to demonstrate their capacity to represent important processes and properties across a broad range of applications, and to provide a template for transcending solutions across the wide range of conditions occurring along boundaries and interfaces. While the mathematical and computational developments necessary to solve each problem are developed in later chapters, each figure documents where its solutions are presented.

Foundation of the Analytic Element Method

2020 ◽  
pp. 71-102
Author(s):  
David R. Steward
Keyword(s):  
General Solution ◽  
Just In Time ◽  
Mathematical Functions ◽  
Analytic Element Method ◽  
Analytic Element ◽  
Solution Methods ◽  
Concise Representation ◽  
Analytic Elements ◽  
Element Method

The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science, where problems are structured around elements to organize mathematical functions and methods. While this text mostly adheres to a ``just in time mathematics'' philosophy, whereby mathematical approaches are introduced when they are first needed, a comprehensive paradigm is presented in Section 2.1 as four steps necessary to achieve solutions. Likewise, Section 2.2 develops general solution methods, and Section 2.3 presents a consistent notation and concise representation to organize analytic elements across the broad range of disciplinary perspectives introduced in Chapter 1.

Pump-and-treat optimization using analytic element method flow models

2006 ◽  
Vol 29 (5) ◽  
pp. 760-775 ◽  
Author(s):  
L. Shawn Matott ◽  
Alan J. Rabideau ◽  
James R. Craig
Keyword(s):  
Analytic Element Method ◽  
Flow Models ◽  
Pump And Treat ◽  
Analytic Element ◽  
Element Method

The superblock approach for the analytic element method

1999 ◽  
Vol 226 (3-4) ◽  
pp. 179-187 ◽  
Author(s):  
O.D.L. Strack ◽  
I. Janković ◽  
R. Barnes
Keyword(s):  
Analytic Element Method ◽  
Analytic Element ◽  
Element Method

Analytic Element Method

2020 ◽  
Author(s):  
David R. Steward
Keyword(s):  
Water Waves ◽  
Separation Of Variables ◽  
Singular Integral Equations ◽  
Basic Principles ◽  
Analytic Element Method ◽  
Synergistic Interactions ◽  
New Methods ◽  
Analytic Element ◽  
Complex Functions ◽  
Element Method

The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the AEM, to provide a template for those interested in pursuing these methods, and to empower readers to extend the AEM paradigm to an even broader range of problems. A comprehensive paradigm: place an element within its landscape, formulate its interactions with other elements using linear series of influence functions, and then solve for its coefficients to match its boundary and interface conditions with nearly exact precision. Collectively, sets of elements interact to transform their environment, and these synergistic interactions are expanded upon for three common types of problems. The first problem studies a vector field that is directed from high to low values of a function, and applications include: groundwater flow, vadose zone seepage, incompressible fluid flow, thermal conduction and electrostatics. A second type of problem studies the interactions of elements with waves, with applications including water waves and acoustics. A third type of problem studies the interactions of elements with stresses and displacements, with applications in elasticity for structures and geomechanics. The Analytic Element Method paradigm comprehensively employs a background of existing methodology using complex functions, separation of variables and singular integral equations. This text puts forth new methods to solving important problems across engineering and science, and has a tremendous potential to broaden perspective and change the way problems are formulated.

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