In recent years, new and more effective procedures for applying collocation have been published. This article is devoted to present a revision of this subject and complement its developments. From the general theory two broad approaches are derived, which yield the direct and the indirect TH-collocation methods. The former approach had not been published before, and it is a dual of the indirect approach. In particular, second order differential equations of elliptic type are considered and several orthogonal collocation algorithms are developed for them. In TH-collocation, the approximations on the internal boundary and in the subdomain interiors are completely independent. This yields clear computational advantages that are illustrated through the construction of such algorithms. In the implementations presented, three dimensional problems are included. In passing, single-point-collocation methods that have been the subject of several recent publications are revised. 相似文献
The mechanism and kinetics of the carbothermic reduction of a natural chromite was studied at 1300–1500 °C in the presence of silica. Thermogravimetry, X-ray diffraction (XRD) analysis, energy dispersive X-ray analysis (EDAX) and metallography were the experimental techniques used. Silica affected the reduction at and above 1400 °C. A two stage reduction mechanism was established. The first stage, up to about 40% reduction, is primarily limited to iron metallization and zoning is observed in partially reduced chromites. In this stage silica does not interfere with the reduction. The second stage is mainly confined to chromium metallization and formation of a silicate slag alters the reduction mechanism. Ion-exchange reactions between the reducible cations (Cr3+ and Fe2+) in the spinel and the dissolved cations (A13+ and Mg2+) in the slag allow further reduction. Due to the very high driving force for the diffusion, the overall process is shifted toward a more chemical reaction controlled mechanism. A generalized rate equation was then applied to the individual metallization curves of iron and chromium from which respective rate constants and diffusion coefficients were derived. The rate constants were in the range 6.74 × 10−4–9.01 × 10−4 s−1 for iron and 7.20 × 10−4–8.50 × 10−4 s−1 for chromium reduction at 1500 °C in the presence of silica. At 1500 °C, the corresponding diffusion coefficients were in the range 3.14 × 10−8–4.78 × 10−8 m2/s for Fe2+ diffusion in the spinel and in the range 1.70 × 10−8–2.03 × 10−8 m2/s for the respective diffusion of Cr3+. Finally using Arrhenius plots activation energies were derived. 相似文献
The purpose of this study was to explore the value of extraction of tumor features in contrast-enhanced ultrasonography (CEUS) images based on the deep belief networks (DBN) for the diagnosis of cervical cancer patients and realize the intelligent evaluation on effects of diagnosis and chemotherapy of the cervical cancer. An automatic extraction algorithm with the time-intensity curve (TIC) was proposed based on Sparse nonnegative matrix factorization (SNMF) in this study, and was applied to the framework of automatic analysis of cervical cancer tumors based on the deep belief networks, to assist doctors in the analysis of cervical cancer tumors. The framework was applied to the real clinical diagnostic data, and the feasibility of the method was verified by comparing the accuracy, sensitivity, and specificity. Later, the parameters of patients’ time to peak (TP), peak intensity (PI), mean transit time (MTT), and area under the curve (AUC) were obtained by drawing TICs, and the changes of p53 protein and ki-67 protein obtained by pathological section staining were analyzed to evaluate the therapeutic effect in the patients. It was found that the proposed model of tumor feature extraction based on the DBN had the higher accuracy (86.36%), sensitivity (83.33%), and specificity (87.50%). The related parameters of TIC curve obtained based on SNMF showed that there was a significant difference in p53 content between tissues with different degrees of disease (p?<?0.05), the PI of poorly differentiated tissues was significantly higher than that of those with high to medium differentiation (p?<?0.05). In addition, PI and AUC of patients after chemotherapy were significantly lower than that before chemotherapy (p?<?0.05), while MTT was significantly higher than that before chemotherapy (p?<?0.05). Therefore, the proposed TIC feature extraction of CEUS images based on SNMF and the automatic tumor classification based on deep learning can be used in the diagnosis and efficacy evaluation of cervical cancer patients.
Terrain Visualization is an important part of visualization systems of battlefield, and the visualization of dynamic terrain is also important for dynamic battle environment. In this paper, special attention has been paid on real-time optimally adapting meshes (ROAM) algorithm, which is a candidate for dynamic terrain, and its mesh representation, mesh continuity algorithm and error metrics are discussed. The DEXTER-ROAM algorithm is discussed and analyzed. By revising the mesh representation of ROAM, a dynamic ROAM algorithm based on partial-regular grid is established. By introducing transition region, mesh discontinuity of dynamic partial-regular grid is resolved. Error metric blocks are removed for computation complexity and culling blocks are introduced to accelerate view frustum culling. The algorithm is implemented in a 3D rendering engine called OGRE. In the end, an example of dynamic crater is given to examine the dynamic ROAM algorithm. 相似文献