Items related to A Domain Decomposition Algorithm Based on a Change...
A Domain Decomposition Algorithm Based on a Change to a Hierarchical Basis (Classic Reprint) - Hardcover
Synopsis
A practical approach to faster, better-conditioned finite element systems through a hybrid domain decomposition method.
This book presents a new algorithm that blends hierarchical bases with substructure techniques to improve solver efficiency without heavy matrix transforms.
The method focuses on solving elliptic problems by changing bases only on the interfaces and vertices, keeping interior variables in the standard nodal basis. It shows how this hybrid approach yields a smaller, easier-to-solve system and offers straightforward parallelization opportunities.- Explains the hybrid algorithm that combines hierarchical basis ideas with substructuring.
- Shows how a basis change can reduce the condition number and speed up convergence.
- Discusses practical implementation details, including when and how to apply the change of basis.
- Provides theoretical results and numerical experiments that compare with existing methods.
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