Domain Decomposition
Question
How do overlap and a coarse correction affect convergence, setup cost, and parallel communication?
Planned sequence
- Establish a block-Jacobi baseline for a system from the FEM project.
- Define restriction, extension, overlap, and local subdomain operators.
- Implement additive and restricted additive Schwarz (ASM/RAS).
- Add a two-level correction and state the coarse-space construction.
- Evaluate convergence and communication with the parallel sparse-computing project.
Evidence to record
Report the partition, overlap width, number of subdomains, local solver, coarse-space dimension, outer Krylov method, residual criterion, and timings. State symmetry and definiteness assumptions when selecting the outer solver.
Current evidence
This is a planned project; no ASM/RAS implementation, coarse-space experiment, or scaling claim is published here yet.
Study prerequisites
Basic preconditioners → Domain Decomposition Bridge
Linked notes
No project notes have been published yet. The steps above describe planned work.
Linked paper notes
No paper notes linked yet.