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

  • Book
  • © 2003

Overview

Authors:
  1. Marc Alexander Schweitzer

    1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

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Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 29)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-v
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  2. Introduction

    • Marc Alexander Schweitzer
    Pages 1-11

  3. Partition of Unity Method

    • Marc Alexander Schweitzer
    Pages 13-22

  4. Treatment of Elliptic Equations

    • Marc Alexander Schweitzer
    Pages 23-49

  5. Multilevel Solution of the Resulting Linear System

    • Marc Alexander Schweitzer
    Pages 51-96

  6. Tree Partition of Unity Method

    • Marc Alexander Schweitzer
    Pages 97-126

  7. Parallelization and Implementational Details

    • Marc Alexander Schweitzer
    Pages 127-153

  8. Concluding Remarks

    • Marc Alexander Schweitzer
    Pages 155-159

  9. Back Matter

    Pages 161-199
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Keywords

About this book

the solution or its gradient. These new discretization techniques are promising approaches to overcome the severe problem of mesh-generation. Furthermore, the easy coupling of meshfree discretizations of continuous phenomena to dis­ crete particle models and the straightforward Lagrangian treatment of PDEs via these techniques make them very interesting from a practical as well as a theoretical point of view. Generally speaking, there are two different types of meshfree approaches; first, the classical particle methods [104, 105, 107, 108] and second, meshfree discretizations based on data fitting techniques [13, 39]. Traditional parti­ cle methods stem from physics applications like Boltzmann equations [3, 50] and are also of great interest in the mathematical modeling community since many applications nowadays require the use of molecular and atomistic mod­ els (for instance in semi-conductor design). Note however that these methods are Lagrangian methods; i. e. , they are based On a time-dependent formulation or conservation law and can be applied only within this context. In a particle method we use a discrete set of points to discretize the domain of interest and the solution at a certain time. The PDE is then transformed into equa­ tions of motion for the discrete particles such that the particles can be moved via these equations. After time discretization of the equations of motion we obtain a certain particle distribution for every time step.

Authors and Affiliations

  • Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Marc Alexander Schweitzer

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