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[ FreeCourseWeb.com ] Numerical Methods and Software Tools in Industrial Mathematics  

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English | PDF | 1997 | 404 Pages | ISBN : 081763973X | 34.65 MB

During the last fifty years, the development of better numerical methods and more powerful computers has been a major enterprise for the scien- tific community. Today, problems of extreme complexity can be solved. However, for real life applications, the availability of reliable scientific soft- ware seems to be emerging as a limiting factor.
The main contribution of this book is the discussion on how modern concepts in computer science can be applied in order to develop scientific software that is easier to ex- tend, maintain and use than the traditional counterparts. In addition, new models and methods for challenging problems in industrial mathematics ranging from multiphase flow problems and modelling of solidification pro- cesses to surface modelling based on geological or medical data, are derived and discussed in light of the new software concepts.
The articles in this book present the main results from research programs granted by the Research Council of Norway for the period 1992-1996. These research programs have been carried out in close collaboration between the Department of Mathematics and the Department of Informatics at the University of Oslo, and SINTEF Applied Mathematics, which is a private research institute.
This book is separated into three parts.
Part I - Numerical Software Tools is concerned with the use of object- oriented programming techniques for numerical applications; in particular we focus on the use of C++. An object-oriented software library for linear algebra calculations, an object-oriented software toolkit Siscat for scattered data approximation, and a comprehensive set of tools Diffpack for solving partial differential equations are presented. Part I is concluded by a paper discussing the numerical efficiency of C++ in scientific computing.
Part II - Partial Differential Equations contains eight papers ranging from the modelling of physical phenomena to efficient solvers for algebraic equations arising from the discretization of partial differential equations. The Diffpack software, described in Part I, is extensively used to solve problems arising in models of alloy solidification, spinning of polymer fibers and two-phase flow in heterogeneous porous media. A novel method using splines in the modelling of nonlinear water waves is introduced, and the final papers describe progress in the application of various Krylov subspace iterations methods.
Part III - Geometric Modelling contains six papers ranging from scat- tered data approximation to intersection of manifolds. The Sis cat library, described in Part I, is applied on problems concerning construction and representation of surfaces from scattered data and 3D reconstruction from contour data. Topics within surface interrogation, like manifold intersec- tion and functionality for surface editing, are also covered. Applications are taken from areas like modelling of geometric objects from measurement data, mapping, medicine and computer aided geometric design (CAGD).

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