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A First Course in Boundary Element Methods [electronic resource] / by Steven L. Crouch, Sofia G. Mogilevskaya

Author
Crouch, Steven L.
Published
Cham : Springer Nature Switzerland : Imprint: Springer, 2024.
Edition
1st ed. 2024.
Physical Description
XIV, 477 p. 112 illus. online resource
Additional Creators
Mogilevskaya, Sofia G. and SpringerLink (Online service)
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Series
Contents
1. An Illustration of the Boundary Element Approach -- 2. Potential Theory -- 3. The Direct Boundary Integral Method for Laplace's Equation -- 4. Elasticity -- 5. The Stress Discontinuity Method.
Summary
This textbook delves into the theory and practical application of boundary integral equation techniques, focusing on their numerical solution for boundary value problems within potential theory and linear elasticity. Drawing parallels between single and double layer potentials in potential theory and their counterparts in elasticity, the book introduces various numerical procedures, namely boundary element methods, where unknown quantities reside on the boundaries of the region of interest. Through the approximation of boundary value problems into systems of algebraic equations, solvable by standard numerical methods, the text elucidates both indirect and direct approaches. While indirect methods involve single or double layer potentials separately, yielding physically ambiguous results, direct methods combine potentials using Green's or Somigliana's formulas, providing physically meaningful solutions. Tailored for beginning graduate students, this self-contained textbook offers detailed analytical and numerical derivations for isotropic and anisotropic materials, prioritizing simplicity in presentation while progressively advancing towards more intricate mathematical concepts, particularly focusing on two-dimensional problems within potential theory and linear elasticity.
Subject(s)
ISBN
9783031633416
Digital File Characteristics
text file PDF
Part Of
Springer Nature eBook
View MARC record | catkey: 45331718