Non-Standard Multigrid Techniques Using Checkered Relaxation and Intermediate Grids

Foerster, Hartmut; Stüben, Klaus; Trottenberg, Ulrich

doi:10.1016/b978-0-12-632620-8.50027-9

Cited by 25 publications

(17 citation statements)

References 6 publications

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“…Our analysis refers to multigrid methods where the mesh-size ratio is \/2 [3], [7], [16]. Similar investigations for algorithms with mesh ratio 2 are found in [18].…”

mentioning

confidence: 65%

“…Here r Gauss-Seidel relaxation sweeps are partly performed before the correction step and partly after it. Another half-step is added, because it simplifies the transfer to the coarse grid [3], [7]. We may abandon the discussion of the numerical realization of Algorithm 6.1, because this can be found in [3, Section 2] and in [16].…”

Section: Figurementioning

confidence: 99%

“…The investigations of the second type, e.g. [4], [7], [11], [16], establish explicit and promising bounds for the convergence rate by Fourier methods; but they are restricted to rectangular domains.…”

mentioning

confidence: 99%

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The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation

Braess¹

1984

Math. Comp.

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Abstract. The convergence rate of a multigrid method for the numerical solution of the Poisson equation on a uniform grid is estimated. The results are independent of the shape of the domain as long as it is convex and polygonal. On the other hand, pollution effects become apparent when the domain contains reentrant corners. To estimate the smoothing of the Gauss-Seidel relaxation, the smoothness is measured by comparing the energy norm with a (weaker) discrete seminorm.

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“…Our analysis refers to multigrid methods where the mesh-size ratio is \/2 [3], [7], [16]. Similar investigations for algorithms with mesh ratio 2 are found in [18].…”

mentioning

confidence: 65%

Section: Figurementioning

confidence: 99%

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The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation

Braess¹

1984

Math. Comp.

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“…For the second order approximation, we first relax all the points (x, y) with / j even, then all the points with i/ j odd. Foerster, Stiiben and Trottenberg [13] have shown that this method speeds up the rate of convergence by a factor of two for Poisson's equation with Gauss-Seidel smoothing, compared with lexicographic ordering.…”

Section: (I+)mentioning

confidence: 99%

A Multigrid Continuation Method for Elliptic Problems with Folds

Bolstad¹,

Keller²

1986

SIAM J. Sci. and Stat. Comput.

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Abstract. We introduce a new multigrid continuation method for computing solutions of nonlinear elliptic eigenvalue problems which contain limit points (also called turning points or folds). Our method combines the frozen tau technique of Brandt with pseudo-arc length continuation and correction of the parameter on the coarsest grid. This produces considerable storage savings over direct continuation methods, as well as better initial coarse grid approximations, and avoids complicated algorithms for determining the parameter on finer grids. We provide numerical results for second, fourth and sixth order approximations to the two-parameter, two-dimensional stationary reaction-diffusion problem:For the higher order interpolations we use bicubic and biquintic splines. The convergence rate is observed to be independent of the occurrence of limit points.

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“…We use "non-standard" multigrid techniques introduced by Foerster, Stuben and Trottenberg [6] and developed by Foerster and Witsch [5].…”

Section: Multigrid Componentsmentioning

confidence: 99%

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Phillips

1984

Journal of Computational Physics

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Non-Standard Multigrid Techniques Using Checkered Relaxation and Intermediate Grids

Cited by 25 publications

References 6 publications

The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation

The convergence rate of a multigrid method with Gauss-Seidel relaxation for the Poisson equation

A Multigrid Continuation Method for Elliptic Problems with Folds

Numerical solution of a coupled pair of elliptic equations from solid state electronics

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