Multilevel Additive Methods for Elliptic Finite Element Problems

Maksymilian Dryja, Olof B. Widlund

ISBN 10: 1333584350 / ISBN 13: 9781333584351

Published by Forgotten Books, 2018

About this Item

Print on Demand. This book explores the latest mathematical techniques for solving complex elliptic finite element problems. It is an invaluable resource for researchers and practitioners designing and analyzing methods for solving systems of linear algebraic equations resulting from the finite element approximations of second-order, elliptic problems. The author focuses on additive Schwarz methods, which form an essential class of domain decomposition methods. By providing a general framework for this method, the book reveals new possibilities in designing and analyzing novel iterative methods for solving elliptic finite element problems. The author carefully analyzes the convergence rate and makes recommendations for implementation. Additionally, the book discusses potential topics for future research, making it an excellent reference for anyone looking to delve into this field. The insights provided contribute to the advancement of numerical methods for solving elliptic finite element problems. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781333584351_0

Bibliographic Details

• Title: Multilevel Additive Methods for Elliptic Finite Element Problems
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1333584350
• ISBN 13: 9781333584351
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Calculus

About this title

Synopsis

Efficient solvers for elliptic finite element problems, built from overlapping subregions. This book presents a general framework for additive Schwarz methods and shows how they can be applied to solve second‑order elliptic problems on fine finite element meshes. It discusses how to achieve fast convergence with multi‑level and hierarchical strategies, including practical notes on implementation and parallelism.

The text explains how the problem is broken into subspaces, how projections are used to combine local solutions, and why the method’s convergence can be made independent of mesh size and level count. It covers two‑level and multilevel schemes, analyzes condition numbers, and compares several related approaches in a unified framework. The material is written for readers seeking theory and tangible guidance for applying these methods to three‑dimensional problems and beyond.

• Framework: additive Schwarz methods with overlapping subregions in Hilbert spaces


• Two‑level and multilevel algorithms that balance local work with a global coarse solve


• Convergence guarantees and how to control condition numbers across levels


• Connections to other methods like Yserentant’s hierarchical basis and Bramble–Pasciak–Xu approaches

Ideal for readers who want a rigorous, implementable path to scalable solvers for elliptic finite element problems, including researchers and advanced practitioners in numerical analysis and scientific computing.