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1994
Various iterative methods can be classified as domain decomposition methods. Although a prototype of this iteration due to H. A. Schwarz (Viertelsjahresschrift der Naturforschenden Gesellschaft in Zurich, Vol. 15, 1870) is already 120 years old, this class of algorithms has attracted the interest of numerical analysts only recently.
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Various iterative methods can be classified as domain decomposition methods. Although a prototype of this iteration due to H. A. Schwarz (Viertelsjahresschrift der Naturforschenden Gesellschaft in Zurich, Vol. 15, 1870) is already 120 years old, this class of algorithms has attracted the interest of numerical analysts only recently.
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Overlapping Domain Decomposition Methods
2003Overlapping domain decomposition methods are efficient and flexible. It is also important that such methods are inherently suitable for parallel computing. In this chapter, we will first explain the mathematical formulation and algorithmic composition of the overlapping domain decomposition methods. Afterwards, we will focus on a generic implementation
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Multi-level domain decomposition methods
Applied Numerical Mathematics, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Advances in domain decomposition methods
2002Domain decomposition methods (DDM) have received much attention in recent years, which was originally motivated mainly because they are the most effective ways for devising parallel algorithms that can benefit from multiprocessor computation, and supercomputers, in the numerical modeling of continuous systems.
Ismael Herrera, Graciela S. Herrera
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Multigrid Methods of Macrogrid Domain Decomposition
Computational Mathematics and Mathematical PhysicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Algebraic multigrid domain decomposition methods
Russian Journal of Numerical Analysis and Mathematical Modelling, 1989Summary: The paper treats a new approach to constructing multilevel preconditioners for symmetric, positive definite and semi-definite matrices which arises in approximating elliptic problems by finite difference and finite element methods. The approach is based on multilevel domain decomposition methods with partitionings into small substructures and ...
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Molecular imaging in oncology: Current impact and future directions
Ca-A Cancer Journal for Clinicians, 2022Steven P Rowe, Martin G Pomper
exaly
Nonlinear Overlapping Domain Decomposition Methods
2009We discuss some overlapping domain decomposition algorithms for solving sparse nonlinear systemof equations arising fromthe discretization of partial differential equations. All algorithms are derived using the three basic algorithms: Newton for local or global nonlinear systems, Krylov for the linear Jacobian system inside Newton, and Schwarz for ...
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An hybrid domain decomposition method
2007In the field of non overlapping domain decomposition methods, two classical choices are the primal and the dual Schur complement approaches. The first leads to the Balanced Domain Decomposition [1,2] and the second to the Finite Element Tearing and Interconnecting method [3].
Gosselet, Pierre, Rey, Christian
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