ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    On numerical cubatures of singular surface integrals in boundary element methods (1992)
    Springer
    Numerische Mathematik 62 (1992), S. 343-369 
    Details
    ISSN: 0945-3245
    Keywords: 65D30 ; 47G30 ; 45P05 ; 58G15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present and analyze methods for the accurate and efficient evaluation of weakly, Cauchy and hypersingular integrals over piecewise analytic curved surfaces in ℝ3. The class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three-dimensional domains by the boundary integral equation method. The possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point. This rules out weighted quadrature approaches with a fixed singular weight. For weakly singular integrals it is shown that Duffy's triangular coordinates leadalways to a removal of the kernel singularity. Also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero. These are based on the Rabinowitz-Richter estimates in connection with an asymptotic estimate of domains of analyticity in ℂ2. It is further shown that the modified extrapolation approach due to Lyness is in the weakly singular case always applicable. Corresponding error and asymptotic work estimates are presented. For the weakly singular as well as for Cauchy and hypersingular integrals which e.g. arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates. These rules are hierarchically constructed from “finite part” integration formulas in radial and Gaussian formulas in angular direction. Again, we show how the Rabinowitz-Richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396234
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation (1992)
    Springer
    Computing 49 (1992), S. 279-301 
    Details
    ISSN: 1436-5057
    Keywords: Primary 65D30 ; 41A55 ; Secondary 65-04 ; 58G15 ; Numerical cubature ; weakly singular ; Cauchy singular and Hadamard finite part integrals ; symbolic manipulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir untersuchen die numerische Auswertung aller singulärer Oberflächenintegrale, die beim 3-dimensionalen Rand element-Verfahren entstehen, theoretisch und numerisch. Die Verwendung von dreiecksbezogenen oder lokalen Polarkoordinaten nach Duffy zusammen mit Gaußscher Tensorproduktquadratur erweist sich als effizient und zu verläßich sowohl für die h-als auch die p-Randelemente, wenn schwach singuläre Integrale vorliegen. Oberflächenintegrale mit Cauchyschen oder starken Singularitäten führen wir mit Hilfe von Symbolmanipulation auf solche mit schwachen Singularitäten zurück.
    Notes: Abstract The numerical integration of all singular surface integrals arising in 3-d boundary element methods is analyzed theoretically and computationally. For all weakly singular integrals arising in BEM, Duffy's triangular or local polar coordinates in conjunction with tensor product Gaussian quadrature are efficient and reliable for bothh-andp-boundary elements. Cauchy- and hypersingular surface integrals are reduced to weakly singular ones by analytic regularization which is done automatically by symbolic manipulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238933
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...