Analytic Element Method
Complex Interactions of Boundaries and Interfaces
(Sprache: Englisch)
"Analytic Element Method" (AEM) assembles a broad range of mathematical and computational approaches to solve important problems in engineering and science.
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"Analytic Element Method" (AEM) assembles a broad range of mathematical and computational approaches to solve important problems in engineering and science.
Klappentext zu „Analytic Element Method “
"Analytic Element Method" (AEM) assembles a broad range of mathematical and computational approaches to solve important problems in engineering and science. As the subtitle "Complex Interactions of Boundaries and Interfaces" suggests, problems are partitioned into sets of elements and methods are formulated to solve conditions along their boundaries and interfaces. Presentation will 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. Computational methods enable boundary and interface conditions of closely interacting elements to be matched with nearly exact precision, commonly to within 8-12 significant digits. Comprehensive solutions provide elements that collectively interact and shape the environment within which they exist. This work is grounded in a wide range of foundational studies, using exact solutions for important boundary value problems. However, the computational capacity of their times limited solutions to idealized problems, commonly involving a single isolated element within a uniform regional background. With the advent of modern computers, such mathematically based methods were passed over by many, in the pursuit of discretized domain solutions using finite element and finite difference methods. Yet, the elegance of the mathematical foundational studies remains, and the rationale for the Analytic Element Method was inspired by the realization that computational advances could also lead to advances in the mathematical methods that were unforeseeable in the past.
Inhaltsverzeichnis zu „Analytic Element Method “
- Analytic Element Method across Fields of Study
- 1: Philosophical Perspective
- 2: Studies of Flow and Conduction
- 3: Studies of Periodic Waves
- 4: Studies of Deformation by Forces
- Further Reading
- Foundation of the Analytic Element Method
- 5: The Analytical Element Method Paradigm
- 6: Solving Systems of Equations to Match Boundary Conditions
- 7: Consistent Notation for Boundary Value Problems
- Further Reading
- Analytic Elements from Complex Functions
- 8: Point Elements in a Uniform Vector Field
- 9: Domains with Circular Boundaries
- 10: Ellipse Elements with Continuity Conditions
- 11: Slit Element Formulation: Courant's Sewing Theorem with Circle Elements
- 12: Circular Arcs and Joukowsky's Wing
- 13: Complex Vector Fields with Divergence and Curl
- 14: Biharmonic Equation and the Kolosov Formulas
- Further Reading
- Analytic Elements from Separation of Variables
- 15: Overview
- 16: Separation for One-Dimensional Problems
- 17: Separation in Cartesian Coordinates
- 18: Separation in Circular-Cylindrical Coordinates
- 19: Separation in Spherical Coordinates
- 20: Separation in Spheroidal Coordinates
- Further Reading
- Analytic Elements from Singular Integral Equations
- 21: Formulation of Singular Integral Equations
- 22: Double Layer Elements
- 23: Single Layer Elements
- 24: Simpler Far-Field Representation
- 25: Polygon Elements
- 26: Curvilinear Elements
- 27: Three-Dimensional Vector Fields
- Further Reading
- A List of Symbols
- B Solutions to Selected Problem Sets
- References
- Index
Autoren-Porträt von David R. Steward
Professor David R. Steward is chair of the Department of Civil and Environmental Engineering at North Dakota State University and holds the Walter B. Booth Distinguished Professorship. Dr. Steward teaches courses in groundwater flow, water resources, hydraulics and engineering mathematics. He is licensed as a Professional Engineer (North Dakota and Minnesota) and a Professional Geoscientist (Texas), and is a Fellow of the American Society of Civil Engineers.Bibliographische Angaben
- Autor: David R. Steward
- 2020, 336 Seiten, Maße: 19,5 x 25,3 cm, Gebunden, Englisch
- Verlag: Oxford University Press
- ISBN-10: 0198856784
- ISBN-13: 9780198856788
- Erscheinungsdatum: 16.09.2020
Sprache:
Englisch
Pressezitat
Review from previous edition Dr. Steward's book Analytic Element Method: Complex Interactions of Boundaries and Interfaces clearly outlines the mathematical foundations of Analytic Element Method (AEM) modeling techniques. The book could serve as a fine text for graduate-level courses on analytic modeling. Charlie Fitts, Fitts Geosolutions, LLC
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