TY - JOUR
T1 - Towards automatic multigrid algorithms for SPD, nonsymmetric and indefinite problems
AU - Shapira, Yair
AU - Israeli, Moshe
AU - Sidi, Avram
PY - 1996/3
Y1 - 1996/3
N2 - 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.
AB - 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.
KW - Automatic multigrid method
KW - Convection-diffusion equation
KW - Discontinuous coefficients
KW - Elliptic PDEs
KW - Indefinite Helmholtz equation
UR - http://www.scopus.com/inward/record.url?scp=0043018476&partnerID=8YFLogxK
U2 - 10.1137/s1064827593258838
DO - 10.1137/s1064827593258838
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AN - SCOPUS:0043018476
SN - 1064-8275
VL - 17
SP - 439
EP - 453
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 2
ER -