numerical integration on the sphere
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... 3.7 Interpolation on Scattered Data in Multidimensions 139 -- 3.8 Laplace Interpolation 150 -- 4 Integration ... ... and Orthogonal Polynomials 179 -- 4.7 Adaptive Quadrature 194 -- 4.8 Multidimensional Integrals 196 ... ... Airy Functions, Spherical -- Bessel Functions 283 -- 6.7 Spherical Harmonics 292 -- 6.8 Fresnel Integrals ... ... , Cosine and Sine Integrals 297 -- 6.9 Dawson’s Integral 302 -- 6.10 Generalized Fermi-Dirac Integrals ... ... Using the FFT 692 -- 13.10 Wavelet Transforms 699 -- 13.11 Numerical Use of the Sampling Theorem 717 ...
3rd ed. xxi, 1235 s. : il. ; 27 cm + 1 CD-ROM
- MeSH
- matematické výpočty počítačové MeSH
- matematika MeSH
- numerická analýza pomocí počítače * MeSH
- Publikační typ
- monografie MeSH
Several constitutive models have been proposed for the description of mechanical behaviour of soft tissues containing collagen fibres. Some of the commonly used approaches accounting for the dispersion of fibre orientations are based on the summation of (mechanical) contributions of differently oriented fibre families. This leads to the need of numerical integration on the sphere surface, and the related numerical consumption is the main disadvantage of this category of constitutive models. The paper is focused on the comparison of various numerical integration methods applied to a specific constitutive model applicable for arterial walls. Robustness and efficiency of several integration rules were tested with respect to application in finite element (FE) codes. Among all the analysed numerical integration rules, the best results were reached by Lebedev quadrature; the related parameters for the specific constitutive model are presented in the paper. The results were implemented into the commercial FE code ANSYS via user subroutines, and their applicability was demonstrated by an example of FE simulation with non-homogenous stress field.
... The dielectric constant of water 81 -- 5.2 The electric field and voltage of a charged conducting sphere ... ... -- A1.3 Vectors 255 -- Al.4 Vector products 257 xii Contents -- Al.5 Vector calculus 258 -- A1.6 Integrals ... ... 274 -- A3.5 The tension in an ‘entropic chain’ 277 -- Appendix 4: Hints for the solution of and numerical ...
xii, 286 s.
