Finite Element Methods (Computational Mathematics and Applications) by Hans Rudolf Schwarz, Caroline M. Whiteman
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This book is divided into six chapters. In the first some typical simple problems from the range of applications are presented, with as much of the mathematical and physical fundamentals as is needed for the solution of the problems. Whenever possible external principles are used, and when this cannot be done the method of Galerkin serves as the basis for the method of finite elements. Ther second and most extensive chapter deals with the finite elements themselves and shows how the contributions from the different parts of the problem can be made available in am efficient and numerically stable way. The third chapter treats the construction of the corresponding matrices and constant vectors of the complete problem. Some useful hints are given for the implementation of the procedure on a computer. We show how to reduce the order of the resulting algebraic systems and make them easier to solve by optimally numbering the unknowns and eliminating those that can be dropped. In the fourth and fifth chapters practical methods for he numerical solution od large systems od sparse linear equations and eigenvalue problems are described in such a way that the algorithmic formulations allow them to be readily implemented in computer programs. Some of the techniques presented can be found elsewhere only in journals and technical reports. The last chapter contains numerical and graphical results for several practical applications, but are also simple and clear enough to be solvable by the methods presented in previous chapters. It is hoped that the examples given are stimulating enough to motivate readers to solve similar problems of their own choice.
by Hans Rudolf Schwarz, Caroline M. Whiteman
Finite Element Methods (Computational Mathematics and Applications)
Academic Pr (August 1, 1988)
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