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Journal of Scientific Computing

Erschienen in:

01.01.2021

Linear Convergence of a Rearrangement Method for the One-dimensional Poisson Equation

verfasst von: Chiu-Yen Kao, Seyyed Abbas Mohammadi, Braxton Osting

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2021

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Abstract

In this paper, we study a rearrangement method for solving a maximization problem associated with Poisson’s equation with Dirichlet boundary conditions. The maximization problem is to find the forcing within a certain admissible set as to maximize the total displacement. The rearrangement method alternatively (i) solves the Poisson equation for a given forcing and (ii) defines a new forcing corresponding to a particular super-level-set of the solution. Rearrangement methods are frequently used for this problem and a wide variety of similar optimization problems due to their convergence guarantees and observed efficiency; however, the convergence rate for rearrangement methods has not generally been established. In this paper, for the one-dimensional problem, we establish linear convergence. We also discuss the higher dimensional problem and provide computational evidence for linear convergence of the rearrangement method in two dimensions.

Vorheriger Artikel A Novel Parallel Computing Strategy for Compact Difference Schemes with Consistent Accuracy and Dispersion

Nächster Artikel FFT-Based High Order Central Difference Schemes for Poisson’s Equation with Staggered Boundaries

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Titel: Linear Convergence of a Rearrangement Method for the One-dimensional Poisson Equation
verfasst von: Chiu-Yen Kao
Seyyed Abbas Mohammadi
Braxton Osting
Publikationsdatum: 01.01.2021
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2021
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01389-5

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