Discretization Methods and Iterative Solvers Based on Domain Decomposition
Edition: 1 edition
Publisher: Springer
Published: March 26, 2001
Language: eng
Format: Paperback
Number of pages: 197
ISBN-13: 9783540410836
Subjects: Differential Equations; Numerical analysis; Mathematics; Analytic Mechanics (Mathematical Aspects); Partial Differential Equations; Science/Mathematics; Probability & Statistics - General; Numerical solutions; Applied; General; Domain decomposition techniques; Mathematics / Applied; Schwarz methods; linear elasticity; mortar finite elements; multigrid methods; Advanced; Decomposition method
Description: Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.
Notes: Lecture Notes in Computational Science and Engineering