### Abstract

We discuss the problem of solving large linear systems of equations that arise in lattice systems with disorder. Three examples of this kind of problem are (i) computing currents in a random-resistor network, (ii) computing the fermion (quark) propagator in lattice quantum chromodynamics, and (iii) the discrete Schrödinger operator with a random potential (the Anderson model of localization). We show that the algebraic multigrid is a very effective way to compute currents in a random-resistor network. It is likely that similar techniques will apply to the other problems.

Original language | English (US) |
---|---|

Pages (from-to) | 1333-1335 |

Number of pages | 3 |

Journal | Physical Review Letters |

Volume | 61 |

Issue number | 12 |

DOIs | |

State | Published - 1988 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*61*(12), 1333-1335. https://doi.org/10.1103/PhysRevLett.61.1333

**Multigrid method for the random-resistor problem.** / Edwards, Robert G.; Goodman, Jonathan; Sokal, Alan D.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 61, no. 12, pp. 1333-1335. https://doi.org/10.1103/PhysRevLett.61.1333

}

TY - JOUR

T1 - Multigrid method for the random-resistor problem

AU - Edwards, Robert G.

AU - Goodman, Jonathan

AU - Sokal, Alan D.

PY - 1988

Y1 - 1988

N2 - We discuss the problem of solving large linear systems of equations that arise in lattice systems with disorder. Three examples of this kind of problem are (i) computing currents in a random-resistor network, (ii) computing the fermion (quark) propagator in lattice quantum chromodynamics, and (iii) the discrete Schrödinger operator with a random potential (the Anderson model of localization). We show that the algebraic multigrid is a very effective way to compute currents in a random-resistor network. It is likely that similar techniques will apply to the other problems.

AB - We discuss the problem of solving large linear systems of equations that arise in lattice systems with disorder. Three examples of this kind of problem are (i) computing currents in a random-resistor network, (ii) computing the fermion (quark) propagator in lattice quantum chromodynamics, and (iii) the discrete Schrödinger operator with a random potential (the Anderson model of localization). We show that the algebraic multigrid is a very effective way to compute currents in a random-resistor network. It is likely that similar techniques will apply to the other problems.

UR - http://www.scopus.com/inward/record.url?scp=4243875650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243875650&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.61.1333

DO - 10.1103/PhysRevLett.61.1333

M3 - Article

VL - 61

SP - 1333

EP - 1335

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 12

ER -