Towards automatic multigrid algorithms for SPD, nonsymmetric and indefinite problems

Yair Shapira, Moshe Israeli, Avram Sidi

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


A new multigrid algorithm is constructed for the solution of linear systems of equations which arise from the discretization of elliptic PDEs. It is defined in terms of the difference scheme on the fine grid only, and no rediscretization of the PDE is required. Numerical experiments show that this algorithm gives high convergence rates for several classes of problems: symmetric, nonsymmetric and problems with discontinuous coefficients, nonuniform grids, and nonrectangular domains. When supplemented with an acceleration method, good convergence is achieved also for pure convection problems and indefinite Helmholtz equations.

Original languageEnglish
Pages (from-to)439-453
Number of pages15
JournalSIAM Journal on Scientific Computing
Issue number2
StatePublished - Mar 1996
Externally publishedYes


  • Automatic multigrid method
  • Convection-diffusion equation
  • Discontinuous coefficients
  • Elliptic PDEs
  • Indefinite Helmholtz equation


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