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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals (Lecture Notes in Engineering, 73) - Softcover
Synopsis
In three dimensional boundary element analysis, computation of integrals is an important aspect since it governs the accuracy of the analysis and also because it usually takes the major part of the CPU time. The integrals which determine the influence matrices, the internal field and its gradients contain (nearly) singular kernels of order lIr a (0:= 1,2,3,4,.··) where r is the distance between the source point and the integration point on the boundary element. For planar elements, analytical integration may be possible 1,2,6. However, it is becoming increasingly important in practical boundary element codes to use curved elements, such as the isoparametric elements, to model general curved surfaces. Since analytical integration is not possible for general isoparametric curved elements, one has to rely on numerical integration. When the distance d between the source point and the element over which the integration is performed is sufficiently large compared to the element size (d> 1), the standard Gauss-Legendre quadrature formula 1,3 works efficiently. However, when the source is actually on the element (d=O), the kernel 1I~ becomes singular and the straight forward application of the Gauss-Legendre quadrature formula breaks down. These integrals will be called singular integrals. Singular integrals occur when calculating the diagonals of the influence matrices.
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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals (Paperback)
Published by
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1992
ISBN 10: 3540550003
ISBN 13: 9783540550006
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Seller: Grand Eagle Retail, Mason, OH, U.S.A.
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Paperback. Condition: new. Paperback. This study proposes a numerical integration method for nearly singular integrals over general curved surfaces, arising in three dimensional boundary element analysis. Nearly singular integrals frequently occur in engineering problems involving thin structures of gaps and when calculating the field near the boundary. Numerical experiments show that the method is far more efficient compared to previous methods and is robust concerning the type of integral kernel and position of the source point. Theoretical error estimates for the method are derived using complex function theory. The method is also shown to be applicable to weakly singular and hypersingular integrals. Knowledge in basic calculus is assumed. The book is intended for engineers and researchers using the boundary element method who require accurate methods for numerical integration and also for numerical analysts interested in an application area for numerical integration. In three dimensional boundary element analysis, computation of integrals is an important aspect since it governs the accuracy of the analysis and also because it usually takes the major part of the CPU time. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9783540550006
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Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals
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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals (Lecture Notes in Engineering, 73)
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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals (Lecture Notes in Engineering, 73)
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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals
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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals
Published by
Springer Berlin Heidelberg Mrz 1992, 1992
ISBN 10: 3540550003
ISBN 13: 9783540550006
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In three dimensional boundary element analysis, computation of integrals is an important aspect since it governs the accuracy of the analysis and also because it usually takes the major part of the CPU time. The integrals which determine the influence matrices, the internal field and its gradients contain (nearly) singular kernels of order lIr a (0:= 1,2,3,4, ) where r is the distance between the source point and the integration point on the boundary element. For planar elements, analytical integration may be possible 1,2,6. However, it is becoming increasingly important in practical boundary element codes to use curved elements, such as the isoparametric elements, to model general curved surfaces. Since analytical integration is not possible for general isoparametric curved elements, one has to rely on numerical integration. When the distance d between the source point and the element over which the integration is performed is sufficiently large compared to the element size (d 1), the standard Gauss-Legendre quadrature formula 1,3 works efficiently. However, when the source is actually on the element (d=O), the kernel 1I~ becomes singular and the straight forward application of the Gauss-Legendre quadrature formula breaks down. These integrals will be called singular integrals. Singular integrals occur when calculating the diagonals of the influence matrices. 468 pp. Englisch. Seller Inventory # 9783540550006
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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals
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A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals
Published by
Springer Berlin Heidelberg, 1992
ISBN 10: 3540550003
ISBN 13: 9783540550006
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In three dimensional boundary element analysis, computation of integrals is an important aspect since it governs the accuracy of the analysis and also because it usually takes the major part of the CPU time. The integrals which determine the influence matri. Seller Inventory # 4893410
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Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals
Published by
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1992
ISBN 10: 3540550003
ISBN 13: 9783540550006
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Softcover
Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, Ireland
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Condition: New. This monograph proposes a numerical integration method for nearly singular integrals over general curved surfaces, arising in three-dimensional boundary element analysis. The method is also applied to weakly singular and hypersingular integrals. A knowledge of calculus is assumed. Series: Lecture Notes in Engineering. Num Pages: 456 pages, 68 black & white tables, biography. BIC Classification: PBKL; TBC; TBJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 242 x 170 x 24. Weight in Grams: 793. . 1992. Softcover reprint of the original 1st ed. 1992. Paperback. . . . . Seller Inventory # V9783540550006
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