Martin Weiser: Adaptive Numerical Solution of PDEs, Kartoniert / Broschiert

Beschreibung

Numerical mathematics is a subtopic ofscientific computing. The focuslies on the efficiencyof algorithms, i. e. speed, reliability, and robustness. This leads to adaptive algorithms. The theoreticalderivation und analysesof algorithmsare kept as elementary as possible in this book; the neededsligtly advancedmathematical theory is summarized in the appendix. Numerous figures and illustrating examples explain the complex data, as non-trivial examples serve problems from nanotechnology, chirurgy, and physiology. The bookaddressesstudents as well aspractitioners inmathematics, naturalsciences, and engineering. It is designed as atextbook but also suitable for self study.

Klappentext

This book deals with the general topic ¿Numerical solution of partial differential equations (PDEs)¿ with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like ¿Numerical Analysis in Modern Scientific Computing¿ by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i. e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.