A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations

✍ Scribed by Marc Alexander Schweitzer (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2003
• Tongue: English
• Leaves: 196
• Series: Lecture Notes in Computational Science and Engineering 29
• Edition: 1
• Category: Library

✦ Synopsis

The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. Up to now, however, meshfree methods have been in an early experimental stage and were not competitive due to the lack of efficient iterative solvers and numerical quadrature. This volume now presents an efficient parallel implementation of a meshfree method, namely the partition of unity method (PUM). A general numerical integration scheme is presented for the efficient assembly of the stiffness matrix as well as an optimal multilevel solver for the arising linear system. Furthermore, detailed information on the parallel implementation of the method on distributed memory computers is provided and numerical results are presented in two and three space dimensions with linear, higher order and augmented approximation spaces with up to 42 million degrees of freedom.

✦ Table of Contents

Front Matter....Pages i-v
Introduction....Pages 1-11
Partition of Unity Method....Pages 13-22
Treatment of Elliptic Equations....Pages 23-49
Multilevel Solution of the Resulting Linear System....Pages 51-96
Tree Partition of Unity Method....Pages 97-126
Parallelization and Implementational Details....Pages 127-153
Concluding Remarks....Pages 155-159
Back Matter....Pages 161-199

✦ Subjects

Computational Mathematics and Numerical Analysis;Numerical and Computational Physics;Partial Differential Equations;Appl.Mathematics/Computational Methods of Engineering