Acceleration of the Jacobi iterative method by factors exceeding 100 using scheduled relaxation

Xiyang I.A. Yang, Rajat Mittal

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We present a methodology that accelerates the classical Jacobi iterative method by factors exceeding 100 when applied to the finite-difference approximation of elliptic equations on large grids. The method is based on a schedule of over- and under-relaxations that preserves the essential simplicity of the Jacobi method. Mathematical conditions that maximize the convergence rate are derived and optimal schemes identified. The convergence rate predicted from the analysis is validated via numerical experiments. The substantial acceleration of the Jacobi method enabled by the current method has the potential to significantly accelerate large-scale simulations in computational mechanics, as well as other areas where elliptic equations are prominent.

Original languageEnglish (US)
Pages (from-to)695-708
Number of pages14
JournalJournal of Computational Physics
StatePublished - Oct 1 2014

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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