A note on MGR methods

Ries, Manfred; Trottenberg, Ulrich; Winter, Gerd

doi:10.1016/0024-3795(83)90091-5

Cited by 65 publications

(60 citation statements)

References 5 publications

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“…A typical result from Table 1 in Section 6 shows that the convergence rate is 0.172 or better, when at least one Gauss-Seidel relaxation step per cycle is performed for the smoothing. Our result is not far from the number 0.125 which was recently determined as the asymptotic convergence rate for rectangular domains [16]. The given rate guarantees quick convergence of the multigrid iteration with IP-cycles.…”

supporting

confidence: 50%

“…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: 79%

“…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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supporting

confidence: 50%

“…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: 79%

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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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“…We note that for the Poisson equation the bound for the two-grid contraction number of our method (cf. Remark 3.6.1) is the same as for the two-grid methods in [11,3,4]. In these papers red-black coarsening and a matrix-dependent prolongation are used too.…”

Section: Two-and 1nultigrid Methodmentioning

confidence: 99%

“…(3.14) based on the Galerkin condition. The bound for the Poisson equation as in Remark 3.6.1 holds with damped Ja.cobi smoothing, whereas in [11,3,4] red-black Gauss-Seidel smoothing is used. Finally note that in [11,3,4] the main subject is an analysis of a very efficient multigrid solver for Poisson-like equations, whereas our purpose is to develop a robust and reasonably efficient muitigrid solver for convection-diffusion problems.…”

Section: Two-and 1nultigrid Methodmentioning

confidence: 99%

Multigrid with Matrix-dependent Transfer Operators for Convection-diffusion Problems

Reusken

1994

Multigrid Methods IV

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Protein Contacts and Ligand Binding in the Inward‐Facing Model of Human P‐Glycoprotein

2013

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The primary aim of this work was to analyze the contacts between residues in the nucleotide binding domains (NBDs) and at the interface between the transmembrane domains (TMDs) and the NBDs in the inward-open homology model of human P-glycoprotein (P-gp). The analysis revealed communication nets through hydrogen bonding in the NBD and at the NBD-TMD interface of each half involving residues from the adenosine triphosphate (ATP) motifs and the coupling helices of the intracellular loops. Similar networks have been identified in P-gp conformations generated by molecular dynamics simulation. Differences have been recorded in the networking between both halves of P-gp. Many of the residue contacts have also been observed in the X-ray crystal structures of other ATP binding cassette (ABC) transporters, which confirms their validity. Next, possible binding pockets involving residues of importance for the TMD-NBD communication were identified. By studying these pockets, binding sites were suggested for rhodamine 123 (R-site) and prazosin (regulatory site) at the NBD-TMD interface that agreed with the experimental data on their location. Additionally, one more R-site in the protein cavity was proposed, in accordance with the available biochemical data. Together with the previously suggested Hoechst 33342 site (H-site), all sites were interpreted with respect to their effects on the protein ATPase activity, in correspondence with the experimental observations. Several residues involved in key contacts in the P-gp NBDs were proposed for further targeted mutagenesis experiments.

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A note on MGR methods

Cited by 65 publications

References 5 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

Multigrid with Matrix-dependent Transfer Operators for Convection-diffusion Problems

Protein Contacts and Ligand Binding in the Inward‐Facing Model of Human P‐Glycoprotein

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