03897nam a22005415i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003100118041000800149050001400157050001400171072001600185072002300201082001200224100003100236245011500267260003800382264003800420300003300458336002600491337002600517338003600543347002400579490008800603505014800691520189400839650001702733650002102750650002802771650001702799650002602816650002902842650001702871650005902888650003302947650004402980650004203024650003703066700003003103710003403133773002003167776003603187830008803223856004403311978-0-387-34042-5DE-He21320141014113430.0cr nn 008mamaa100301s2007 xxu| s |||| 0|eng d a97803873404257 a10.1007/0-387-34042-42doi aeng 4aTA329-348 4aTA640-643 7aTBJ2bicssc 7aMAT0030002bisacsh04a5192231 aRjasanow, Sergej.eauthor.14aThe Fast Solution of Boundary Integral Equationsh[electronic resource] /cby Sergej Rjasanow, Olaf Steinbach. 1aBoston, MA :bSpringer US,c2007. 1aBoston, MA :bSpringer US,c2007. aXI, 279 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aMathematical and Analytical Techniques with Applications to Engineering,x1559-74580 aBoundary Integral Equations -- Boundary Element Methods -- Approximation of Boundary Element Matrices -- Implementation and Numerical Examples. aThe use of surface potentials to describe solutions of partial differential equations goes back to the middle of the 19th century. Numerical approximation procedures, known today as Boundary Element Methods (BEM), have been developed in the physics and engineering community since the 1950s. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations. The Fast Solution of Boundary Integral Equations provides a detailed description of fast boundary element methods which are based on rigorous mathematical analysis. In particular, a symmetric formulation of boundary integral equations is used, Galerkin discretisation is discussed, and the necessary related stability and error estimates are derived. For the practical use of boundary integral methods, efficient algorithms together with their implementation are needed. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given which underline both theoretical results and the practical relevance of boundary element methods in typical computations. The most prominent example is the potential equation (Laplace equation), which is used to model physical phenomena in electromagnetism, gravitation theory, and in perfect fluids. A further application leading to the Laplace equation is the model of steady state heat flow. One of the most popular applications of the BEM is the system of linear elastostatics, which can be considered in both bounded and unbounded domains. A simple model for a fluid flow, the Stokes system, can also be solved by the use of the BEM. The most important examples for the Helmholtz equation are the acoustic scattering and the sound radiation. 0aEngineering. 0aComputer vision. 0aDifferential Equations. 0aMathematics. 0aMathematical physics. 0aEngineering mathematics.14aEngineering.24aAppl.Mathematics/Computational Methods of Engineering.24aApplications of Mathematics.24aMathematical and Computational Physics.24aImage Processing and Computer Vision.24aOrdinary Differential Equations.1 aSteinbach, Olaf.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387340418 0aMathematical and Analytical Techniques with Applications to Engineering,x1559-745840uhttp://dx.doi.org/10.1007/0-387-34042-4