03584nam a22005655i 4500 978-3-031-63341-6 DE-He213 20251030112642.0 cr nn 008mamaa 240722s2024 sz | s |||| 0|eng d 9783031633416 978-3-031-63341-6 10.1007/978-3-031-63341-6 doi TA349-359 TGB bicssc TEC009070 bisacsh TGB thema Crouch, Steven L. author. aut http://id.loc.gov/vocabulary/relators/aut 81008 A First Course in Boundary Element Methods [electronic resource] / by Steven L. Crouch, Sofia G. Mogilevskaya. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 477 p. 112 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Engineering, 2192-4740 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. 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. Indirect methods involve single or double layer potentials separately while direct methods combine these potentials using Green's or Somigliana's formulas. The two approaches give comparable results for general boundary value problems. 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. Mechanics, Applied. Mechanical engineering. 58323 Engineering mathematics. 64145 Engineering Data processing. Engineering Mechanics. Mechanical Engineering. 58323 Mathematical and Computational Engineering Applications. Mogilevskaya, Sofia G. author. aut http://id.loc.gov/vocabulary/relators/aut 81009 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031633409 Printed edition: 9783031633423 Printed edition: 9783031633430 Mathematical Engineering, 2192-4740 81010 https://doi.org/10.1007/978-3-031-63341-6 ZDB-2-ENG ZDB-2-SXE 61801 61801