### Abstract

Waveform relaxation techniques for the pseudospectral solution of the heat conduction problem are discussed. The pseudospectral operator occurring in the equation is preconditioned by transformations in both space and time. In the spatial domain, domain stretching is used to more equally distribute the grid points across the domain, and hence improve the conditioning of the differential operator. Preconditioning in time is achieved either by an exponential or a polynomial transformation. Block Jacobi solutions of the systems are obtained and compared. The preconditioning in space by domain stretching determines the effectiveness of waveform relaxation in this case. Preconditioning in time is also effective in reducing the number of iterations required for convergence. The polynomial transformation is preferred, because it removes the requirement of a matrix exponential calculation in the time-stepping schemes and, at the same time, is no less effective than the direct exponential preconditioning.

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

Pages (from-to) | 245-263 |

Number of pages | 19 |

Journal | Numerical Methods for Partial Differential Equations |

Volume | 12 |

Issue number | 2 |

State | Published - 1996 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Computational Mathematics

### Cite this

**The performance of preconditioned waveform relaxation techniques for pseudospectral methods.** / Burrage, K.; Jackiewicz, Zdzislaw; Renaut, Rosemary.

Research output: Contribution to journal › Article

*Numerical Methods for Partial Differential Equations*, vol. 12, no. 2, pp. 245-263.

}

TY - JOUR

T1 - The performance of preconditioned waveform relaxation techniques for pseudospectral methods

AU - Burrage, K.

AU - Jackiewicz, Zdzislaw

AU - Renaut, Rosemary

PY - 1996

Y1 - 1996

N2 - Waveform relaxation techniques for the pseudospectral solution of the heat conduction problem are discussed. The pseudospectral operator occurring in the equation is preconditioned by transformations in both space and time. In the spatial domain, domain stretching is used to more equally distribute the grid points across the domain, and hence improve the conditioning of the differential operator. Preconditioning in time is achieved either by an exponential or a polynomial transformation. Block Jacobi solutions of the systems are obtained and compared. The preconditioning in space by domain stretching determines the effectiveness of waveform relaxation in this case. Preconditioning in time is also effective in reducing the number of iterations required for convergence. The polynomial transformation is preferred, because it removes the requirement of a matrix exponential calculation in the time-stepping schemes and, at the same time, is no less effective than the direct exponential preconditioning.

AB - Waveform relaxation techniques for the pseudospectral solution of the heat conduction problem are discussed. The pseudospectral operator occurring in the equation is preconditioned by transformations in both space and time. In the spatial domain, domain stretching is used to more equally distribute the grid points across the domain, and hence improve the conditioning of the differential operator. Preconditioning in time is achieved either by an exponential or a polynomial transformation. Block Jacobi solutions of the systems are obtained and compared. The preconditioning in space by domain stretching determines the effectiveness of waveform relaxation in this case. Preconditioning in time is also effective in reducing the number of iterations required for convergence. The polynomial transformation is preferred, because it removes the requirement of a matrix exponential calculation in the time-stepping schemes and, at the same time, is no less effective than the direct exponential preconditioning.

UR - http://www.scopus.com/inward/record.url?scp=0007128857&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007128857&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0007128857

VL - 12

SP - 245

EP - 263

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

SN - 0749-159X

IS - 2

ER -