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Titlebook: Boundary Integral Equations; George C. Hsiao,Wolfgang L. Wendland Book 20081st edition Springer-Verlag Berlin Heidelberg 2008 Fredholm alt

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期刊全称Boundary Integral Equations
影响因子2023George C. Hsiao,Wolfgang L. Wendland
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发行地址Includes supplementary material:
学科分类Applied Mathematical Sciences
图书封面Titlebook: Boundary Integral Equations;  George C. Hsiao,Wolfgang L. Wendland Book 20081st edition Springer-Verlag Berlin Heidelberg 2008 Fredholm alt
影响因子This book is devoted to the mathematical foundation of boundary integral equations. The combination of ?nite element analysis on the boundary with these equations has led to very e?cient computational tools, the boundary element methods (see e.g., the authors [139] and Schanz and Steinbach (eds.) [267]). Although we do not deal with the boundary element discretizations in this book, the material presented here gives the mathematical foundation of these methods. In order to avoid over generalization we have con?ned ourselves to the treatment of elliptic boundary value problems. The central idea of eliminating the ?eld equations in the domain and - ducing boundary value problems to equivalent equations only on the bou- ary requires the knowledge of corresponding fundamental solutions, and this idea has a long history dating back to the work of Green [107] and Gauss [95, 96]. Today the resulting boundary integral equations still serve as a major tool for the analysis and construction of solutions to boundary value problems.
Pindex Book 20081st edition
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Ronald R. Rindfuss,Minja Kim Choeort excursion into differential geometry is included. Once the fundamental solution is available, the representation of solutions to the boundary value problems is based on general Green‘s formulae which are formulated in terms of distributions and multilayer potentials on Γ. The latter leads us to
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R. D. Priester Jr.,R. B. Turnere versa. For elliptic pseudodifferential operators, we construct parametrices. For elliptic differential operators, in addition, we construct Levi functions and also fundamental solutions if they exist. Since the latter provide the most convenient basis for boundary integral equation formulations, w
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https://doi.org/10.1007/BFb0119075ass of boundary integral equations for elliptic boundary value problems in applications. In particular, the three–dimensional boundary value problems for the Helmholtz equation in scattering theory, the Lamé equations of linear elasticity and the Stokes system will serve as model problems. Two–dimen
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Boundary Integral Equations,s system and its boundary integral equations. In the two–sdimensional case, both the Stokes and the Lamé problems can be reduced to solutions of biharmonic boundary value problems which, again, can be solved by using boundary integral equations based on the direct approach..In this chapter we consid
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Introduction to Pseudodifferential Operators,e versa. For elliptic pseudodifferential operators, we construct parametrices. For elliptic differential operators, in addition, we construct Levi functions and also fundamental solutions if they exist. Since the latter provide the most convenient basis for boundary integral equation formulations, w
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