Author | Schweitzer, Marc Alexander. author |
---|---|
Title | A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations [electronic resource] / by Marc Alexander Schweitzer |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-642-59325-3 |
Descript | VI, 200 p. 15 illus. online resource |
1 Introduction -- 2 Partition of Unity Method -- 2.1 Construction of a Partition of Unity Space -- 2.2 Properties -- 2.3 Basic Convergence Theory -- 3 Treatment of Elliptic Equations -- 3.1 Galerkin Discretization -- 3.2 Boundary Conditions -- 3.3 Numerical Results -- 4 Multilevel Solution of the Resulting Linear System -- 4.1 Multilevel Iterative Solvers -- 4.2 Multilevel Partition of Unity Method -- 4.3 Numerical Results -- 5 Tree Partition of Unity Method -- 5.1 Single Level Cover Construction -- 5.2 Construction of a Sequence of PUM Spaces -- 5.3 Numerical Results -- 6 Parallelization and Implementational Details -- 6.1 Parallel Data Structures -- 6.2 Parallel Tree Partition of Unity Method -- 6.3 Numerical Results -- 7 Concluding Remarks -- Treatment of other Types of Equations -- A.1 Parabolic Equations -- A.2 Hyperbolic Equations -- Transformation of Keys -- Color Plates -- References