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Meshfree Methods for Partial Differential Equations VI pp 93–109Cite as

Multilevel Partition of Unity Method for Elliptic Problems with Strongly Discontinuous Coefficients

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 89))

Abstract

In this paper, we study the robustness of a multilevel partition of unity method. To this end, we consider a scalar diffusion equation in two and three space dimensions with large jumps in the diffusion coefficient or material properties. Our main focus in this investigation is if the use of simple enrichment functions is sufficient to attain a robust solver independent of the geometric complexity of the material interface.

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Notes

  1. 1.

    There exist more involved extensions of the multigrid approach which are not based on a geometric but on an operator- or matrix-dependent prolongation approach like the black box multigrid [6] or the algebraic multigrid [18] approach. These more involved techniques are specifically designed to be more robust than classical geometric multigrid schemes.

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Authors and Affiliations

  1. Institut für Parallele und Verteilte Systeme, Universität Stuttgart, Universitätsstr. 38, 70569, Stuttgart, Germany

    Marc Alexander Schweitzer

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  1. Marc Alexander Schweitzer
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Correspondence to Marc Alexander Schweitzer .

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Editors and Affiliations

  1. , Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, City, 53115, Germany

    Michael Griebel

  2. Institut für Parallele, und Verteilte Systeme, Universität Stuttgart, Universitätsstraße 38, Stuttgart, 70569, Germany

    Marc Alexander Schweitzer

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Schweitzer, M.A. (2013). Multilevel Partition of Unity Method for Elliptic Problems with Strongly Discontinuous Coefficients. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32979-1_6

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