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steward david r. - analytic element method

Analytic Element Method Complex Interactions of Boundaries and Interfaces




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Genere:Libro
Lingua: Inglese
Pubblicazione: 09/2020





Note Editore

"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.




Sommario

1 - Philosophical Perspective
2 - Studies of Flow and Conduction
3 - Studies of Periodic Waves
4 - Studies of Deformation by Forces
5 - The Analytical Element Method Paradigm
6 - Solving Systems of Equations to Match Boundary Conditions
7 - Consistent Notation for Boundary Value Problems
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
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
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




Autore

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.










Altre Informazioni

ISBN:

9780198856788

Condizione: Nuovo
Dimensioni: 253 x 23.3 x 195 mm Ø 862 gr
Formato: Copertina rigida
Pagine Arabe: 336


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