A parallelizable iterative procedure for the Helmholtz problem.

*(English)*Zbl 0805.65100This paper proposes a finite difference approach for solving the Helmholtz problem. The importance of this approach lies in the use of a parallel computational technique which is known to be suitable for real life applications because of the remarkable speed it provides for the solution to converge. The author supports the proposed technique by sound theoretical foundations and provides tutorials to demonstrate the application of this parallelizable iterative procedure on one- and two- dimensional problems. For this, a method for choosing the algorithm parameters is presented.

This paper makes a good contribution to the field of numerical mathematics and can be successfully implemented by electrical engineers working on high frequency electromagnetic problems and by those interested in the finite difference and parallel computation techniques.

This paper makes a good contribution to the field of numerical mathematics and can be successfully implemented by electrical engineers working on high frequency electromagnetic problems and by those interested in the finite difference and parallel computation techniques.

Reviewer: R.Chedid (Beirut)

##### MSC:

65N06 | Finite difference methods for boundary value problems involving PDEs |

65F10 | Iterative numerical methods for linear systems |

65Y05 | Parallel numerical computation |

65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

78A25 | Electromagnetic theory (general) |

##### Keywords:

Helmholtz equation; finite difference method; iterative procedure; high frequency electromagnetic problems; parallel computation
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##### References:

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