Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

• Main Author: Mathew, Tarek Poonithara Abraham (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Lecture Notes in Computational Science and Engineering, 61
• Subjects: Mathematics.; Computer science > Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Computer mathematics.; Computational intelligence.; Analysis.; Computational Science and Engineering.; Mathematics of Computing.; Computational Intelligence.; Computational Mathematics and Numerical Analysis.; Partial Differential Equations.

Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorithms for solving the discretized equations, techniques for non-matching grid discretizations and techn...

Table of Contents:

• Decomposition Frameworks
• Schwarz Iterative Algorithms
• Schur Complement and Iterative Substructuring Algorithms
• Lagrange Multiplier Based Substructuring: FETI Method
• Computational Issues and Parallelization
• Least Squares-Control Theory: Iterative Algorithms
• Multilevel and Local Grid Refinement Methods
• Non-Self Adjoint Elliptic Equations: Iterative Methods
• Parabolic Equations
• Saddle Point Problems
• Non-Matching Grid Discretizations
• Heterogeneous Domain Decomposition Methods
• Fictitious Domain and Domain Imbedding Methods
• Variational Inequalities and Obstacle Problems
• Maximum Norm Theory
• Eigenvalue Problems
• Optimization Problems
• Helmholtz Scattering Problem.