We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.
We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.
We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.
A time discrete scheme is used to approximate the solution toa phase field system of PenroseFife type with a non-conservedorder parameter. An a posteriori error estimate is presentedthat allows the estimation of the difference between continuousand semidiscrete solutions by quantities that can be calculatedfrom the approximation and given data. 相似文献
The dielectric constant for rain medium is investigated by utilizing the system identification method. The rain rate model and frequency model of permittivity in millimeter waves band for rain medium are presented. The results obtained with models are in very good agreement with references in calculating the attenuation of electromagnetic waves induced by rain, which Shows that the obtained models are valid and practicable. The cross-polar discrimination gotten with rain rate model is in agreement with references. 相似文献
Trabecular bone fracture is closely related to the trabecular architecture, microdamage accumulation, and bone tissue properties. Primary constituents of trabecular tissue are hydroxyapatite (HA) mineralized type-I collagen fibers. In this research, dynamic fracture in two dimensional (2-D) micrographs of ovine (sheep) trabecular bone is modeled using the mesoscale cohesive finite element method (CFEM). The bone tissue fracture properties are obtained based on the atomistic strength analyses of a type-I collagen + HA interfacial arrangement using molecular dynamics (MD). Analyses show that the presented framework is capable of analyzing the architecture dependent fracture in 2-D micrographs of trabecular bone. 相似文献
The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields. 相似文献