03399nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001600186072002300202072001500225100008600240245011700326250001800443264006900461300004500530336002600575337002600601338003600627347002400663490004100687505020200728520130100930650002402231650003502255650003602290650003402326650002702360650003502387650006102422700009102483710003402574773002602608776003602634776003602670776003602706830004802742856004602790912001402836912001402850999001702864978-3-031-63341-6DE-He21320251030112642.0cr nn 008mamaa240722s2024    sz |    s    |||| 0|eng d  a97830316334169978-3-031-63341-67 a10.1007/978-3-031-63341-62doi 4aTA349-359 7aTGB2bicssc 7aTEC0090702bisacsh 7aTGB2thema1 aCrouch, Steven L.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98100812aA First Course in Boundary Element Methodsh[electronic resource] /cby Steven L. Crouch, Sofia G. Mogilevskaya.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIV, 477 p. 112 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aMathematical Engineering,x2192-47400 a1. 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.  aThis 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. 0aMechanics, Applied. 0aMechanical engineering.958323 0aEngineering mathematics.964145 0aEngineeringxData processing.14aEngineering Mechanics.24aMechanical Engineering.95832324aMathematical and Computational Engineering Applications.1 aMogilevskaya, Sofia G.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9810092 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303163340908iPrinted edition:z978303163342308iPrinted edition:z9783031633430 0aMathematical Engineering,x2192-474098101040uhttps://doi.org/10.1007/978-3-031-63341-6  aZDB-2-ENG  aZDB-2-SXE  c61801d61801