Comparison of Linear System Solvers Applied to Diffusion-Type Finite Element Equations (Classic Reprint) - Softcover

Anne Greenbaum

 
9781332868490: Comparison of Linear System Solvers Applied to Diffusion-Type Finite Element Equations (Classic Reprint)

Synopsis

This book explores the performance of various iterative methods for solving the linear systems that arise from the finite element approximations of self-adjoint elliptic partial differential operators. The methods are compared based on their efficiency on serial and parallel machines, offering a comprehensive analysis of their strengths and weaknesses within different computational environments. The author presents a detailed study of several methods, including diagonal scaling, incomplete Cholesky decomposition, hierarchical basis functions, and a Neumann-Dirichlet domain decomposition technique. Numerical results obtained from tests performed on the NYU Ultracomputer Prototype are included, providing valuable insights into the practical performance of these methods. Through its rigorous analysis and practical testing, this book contributes significantly to the field of computational methods for solving partial differential equations, making it a valuable resource for researchers and practitioners in scientific computing, engineering, and applied mathematics.

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