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Titlebook: A First Course in Boundary Element Methods; Steven L. Crouch,Sofia G. Mogilevskaya Book 2024 The Editor(s) (if applicable) and The Author(

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期刊全稱A First Course in Boundary Element Methods
影響因子2023Steven L. Crouch,Sofia G. Mogilevskaya
視頻videohttp://file.papertrans.cn/168/167020/167020.mp4
發(fā)行地址Provides in-depth derivations of key mathematical solutions.Distinguishes itself from conventional boundary element method texts.Offers essential solutions and algorithm insights
學(xué)科分類Mathematical Engineering
圖書封面Titlebook: A First Course in Boundary Element Methods;  Steven L. Crouch,Sofia G. Mogilevskaya Book 2024 The Editor(s) (if applicable) and The Author(
影響因子.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
Pindex Book 2024
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An Illustration of the Boundary Element Approach,several examples are worked to demonstrate the accuracy of the methods. The two boundary element methods in this chapter are called ., because the sources . and . are generally not physically meaningful. It is shown that the methods can also be viewed as numerical representations of integral expressions for single and double layer potentials.
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Elasticity,, as well as limit values for the displacement formula for two dimensions for the case that .. When the boundary . represents a crack, comparable formulas are developed for the displacements, stresses, and tractions at a point . inside . in terms of the displacement discontinuities along the crack. These formulas are attributed to Volterra.
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Potential Theory, terms of single and double layer potentials with density functions equal to (a) the normal derivative of the potential on . and (b) the potential on the same boundary. Expressions are also given for the gradient and normal derivative of the potential . at points . inside region ., as well as limit values of all expressions for the case that ..
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