CADD: A seamless solution to the Domain Decomposition problem of subdomain boundaries and cross-points

Dan Gordon, Rachel Gordon

Research output: Contribution to journalArticlepeer-review


The solution of wave problems using Domain Decomposition (DD) requires that the subdomain boundaries should be virtually non-existent, so that waves are not affected by the boundaries. This is a primary problem in DD, and it intensifies in the case of cross-points at which three or more subdomains meet. This topic has received a lot of attention in recent years, with special treatment of cross-points. This paper explains and demonstrates that this problem does not exist in Component-Averaged Domain Decomposition (CADD). CADD is implemented here with the authors’ CARP-CG algorithm, but it is shown that other implementations are also possible. The reason for the non-existence of this problem in CARP-CG is that in some superspace of the problem space, CARP-CG is mathematically equivalent to the CG acceleration of the Kaczmarz algorithm with cyclic relaxation parameters, applied to a single linear system. Due to its advantages, CARP-CG was adopted by some geophysics researchers as the solver of the Helmholtz and the elastic wave equations for full waveform inversion (FWI).

Original languageEnglish
Article number102649
JournalWave Motion
StatePublished - Nov 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • CADD
  • CARP
  • CGMN
  • Component-averaged domain decomposition
  • Elastic wave equation
  • Helmholtz equation
  • Kaczmarz
  • Linear equations
  • Parallel processing
  • Partial differential equations
  • Sparse systems
  • Wave problems

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Physics and Astronomy
  • Computational Mathematics
  • Applied Mathematics


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