Stationary splitting iterative methods for the matrix equation AX B = C

Stationary splitting iterative methods for solving AXB = Care considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A = M −N by a matrix H such that (I −H) invertible. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned variants. In particular, for certain surface fitting applications, our method is much more efficient than the progressive iterative approximation (PIA), a conventional iterative method often used in computer-aided geometric design (CAGD).The authors would like to thank the supports of the National Natural Science Foundation of China under Grant No. 11371075, the Hunan Key Laboratory of mathematical modeling and analysis in engineering, and the Portuguese Funds through FCT–Fundação para a Ciência e a Tecnologia, within the Project UID/MAT/00013/2013

Three-dimensional finite element analysis of earth pressure balance tunnelling

Ph.DDOCTOR OF PHILOSOPH

Empirical Modeling and Its Applications

Empirical modeling has been a useful approach for the analysis of different problems across numerous areas/fields of knowledge. As it is known, this type of modeling is particularly helpful when parametric models, due to various reasons, cannot be constructed. Based on different methodologies and approaches, empirical modeling allows the analyst to obtain an initial understanding of the relationships that exist among the different variables that belong to a particular system or process. In some cases, the results from empirical models can be used in order to make decisions about those variables, with the intent of resolving a given problem in the real-life applications. This book entitled Empirical Modeling and Its Applications consists of six (6) chapters

Deformation studies of the folded myolites of the Moine Thrust, Eriboll district, Northwest Scotland.

An area in the northern part of the Moine Thrust Zone of Loch Eriboll and in the NE side of Loch Hope, NW Scotland, has been mapped in the scale of approximately 1:10,560. Detailed measurements have beea made of structures such as foliations and lineations and these have been studied and analysed geometrically in terms of their relative age and the consistence over the whole area. The mapping has also traced the intricate pattern of thrust faults which trend roughly NNE/SSW. These thrust zones delimit different nappes and the deformation aspects of these faults indicate that the rheology of the rocks suffered changes during the thrust belt evolution. The easternmost major thrust zone is considered to have been developed first and clearly shows the characteristics of a ductile deformation zone. This zone is interpreted here as the Moine Thrust Zone, sensu stricto. A conspicuous mylonitic zone lies beneath and trends parallel to the Moine Thrust Zone and is limited in the west by a thrust which carried the mylonites onto clearly non mylonitic rock. The width of the mylonitic zone varies from Loch Hope in the north to the SE end of Loch Eriboll. This width variation is interpreted as due to thickening of the mylonitic zone by effects of folding and also due to the different deformation bands which anastomose and die out. Closely spaced cross sections, transverse to the extension of the belt of deformation are illustrated and discussed. Strain analyses were carried out in two different domains of the mapped area. In the southern half of the area, where the frequency of folds is high, the distribution of fold hinges in sheath or curvilinear folds were used as strain indicators. Models, numerical methods and computer programmes for this strain evaluation have been thoroughly investigated. A detailed description of the methods used and tests performed with the constructed computer programmes is given. The results are analysed in conjunction with the land geology and structure. For the northerly half of the mapped area, strain estimations have been made using the grain shapes of the Paleozoic quartzites which are common in the two lowermost nappes. A new method for fitting the strain ellipsoid using three orthogonal ellipses was devised. A computer programme making use of this method was constructed and applied to the existent data. An alternative solution is also presented for the case where the fitted surface is not an ellipsoid. The strain results with the above methods are compared with those obtained using other published programmes and methods of strain estimation. . Microtextural variations in the Paleozoic quartzites of the northern domain have been studied. A detailed textural description and correlation is made between the textures and the available information on the deformation intensities shown by the quartz grains. An increase in the measured strain intensity is generally accompanied by an increase in the amount of recrystallized new quartz grains. These facts are consistent with the geology and structures of the nappes where sampling was done. Paleostress estimates using recrystallized grain sizes have been performed at 31 localities in the Eriboll and Hope areas. The methodology of particle-size estimation is described in detail. The necessity for a standardization in the methods of particle-size measurement is emphasized with examples. The estimations of the differential stresses are greater in zones of greater relative deformation intensity. Although there are limitations and some adverse criticisms on the reliability of these paleostress estimates, the conclusion reached by this study is that they form a pattern that fits well with the geology and structure of the investigated area. Rheologic considerations on quartz deformation constitutes the last part of the thesis. Deformation maps were constructed for this study using ranges of probable differential stress and the measured size of the newly recrystallized quartz grains. It is concluded that strain is predominantly accommodated by internal mechanisms operated by dislocation processes. It is also inferred that the operative strain-rate for the deformation conditions of this area, is between 10-13s -1 and 10-12s-