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Boundary Elements Methods (BEM) in the Multidimensional Problems
The boundary element method (BEM) as the apparatus of solution of the boundary‐value problems using the boundary integral equations are divided into three main methods that are distinguished by the approach to the construction of the initial integral equations; direct, indirect, and semi‐direct. The direct BEM leads to the integral equations, which differ from the equations of the indirect method and method of potentials. At the same time a strong connection is outlined between the equations of these methods. Furthermore, the equations have a direct analogy with the methods of structural mechanics: methods of forces, displacements, and initial parameters. The chapter explains how to apply the scheme of a method of delta transformation for the solution of a three‐dimensional problem of the theory of elasticity in order to compare it to the BEM, and the method of potential. It further illustrates the application of spectral method of boundary elements to the solution of multidimensional problems.
Boundary Elements Methods (BEM) in the Multidimensional Problems
The boundary element method (BEM) as the apparatus of solution of the boundary‐value problems using the boundary integral equations are divided into three main methods that are distinguished by the approach to the construction of the initial integral equations; direct, indirect, and semi‐direct. The direct BEM leads to the integral equations, which differ from the equations of the indirect method and method of potentials. At the same time a strong connection is outlined between the equations of these methods. Furthermore, the equations have a direct analogy with the methods of structural mechanics: methods of forces, displacements, and initial parameters. The chapter explains how to apply the scheme of a method of delta transformation for the solution of a three‐dimensional problem of the theory of elasticity in order to compare it to the BEM, and the method of potential. It further illustrates the application of spectral method of boundary elements to the solution of multidimensional problems.
Boundary Elements Methods (BEM) in the Multidimensional Problems
Petrosian, Levon G. (author) / Ambartsumian, Vladimir A. (author)
2020-04-27
38 pages
Article/Chapter (Book)
Electronic Resource
English
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