A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit <a rel="external noopener" href="https://arxiv.org/pdf/2110.11211v2.pdf">the original URL</a>. The file type is <code>application/pdf</code>.
A dimension-oblivious domain decomposition method based on space-filling curves
[article]
<span title="2022-04-20">2022</span>
<i >
arXiv
</i>
<span class="release-stage" >pre-print</span>
Preserved Fulltext
Other Versions
<span title="2021-10-21">2021</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.11211v1">arXiv:2110.11211v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jnstdgv4kzb67npn4z4pizy6ii">fatcat:jnstdgv4kzb67npn4z4pizy6ii</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.11211v1">arXiv:2110.11211v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jnstdgv4kzb67npn4z4pizy6ii">fatcat:jnstdgv4kzb67npn4z4pizy6ii</a> </span>
In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed parallel solver is based on a space-filling curve partitioning approach that is applicable to any discretization, i.e. it directly operates on the assembled matrix equations. Moreover, it allows for the effective use of arbitrary processor numbers independent of the dimension of the underlying partial differential equation
<span class="external-identifiers">
<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.11211v2">arXiv:2110.11211v2</a>
<a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/272s4h2huvdeja4brggtdazdwi">fatcat:272s4h2huvdeja4brggtdazdwi</a>
</span>
more »
... ile maintaining optimal convergence behavior. This is the core property required to attain a sparse grid based combination method with extreme scalability which can utilize exascale parallel systems efficiently. Moreover, this approach provides a basis for the development of a fault-tolerant solver for the numerical treatment of high-dimensional problems. To achieve the required data redundancy we are therefore concerned with large overlaps of our domain decomposition which we construct via space-filling curves. In this paper, we propose our space-filling curve based domain decomposition solver and present its convergence properties and scaling behavior. The results of numerical experiments clearly show that our approach provides optimal convergence and scaling behavior in arbitrary dimension utilizing arbitrary processor numbers.
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220423234226/https://arxiv.org/pdf/2110.11211v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext">
<button class="ui simple right pointing dropdown compact black labeled icon button serp-button">
<i class="icon ia-icon"></i>
Web Archive
[PDF]
<div class="menu fulltext-thumbnail">
<img src="https://blobs.fatcat.wiki/thumbnail/pdf/a8/e2/a8e2ca1da8ee4dbc8fbdd2becb54c2b3eeb45ba5.180px.jpg" alt="fulltext thumbnail" loading="lazy">
</div>
</button>
</a>
<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.11211v2" title="arxiv.org access">
<button class="ui compact blue labeled icon button serp-button">
<i class="file alternate outline icon"></i>
arxiv.org
</button>
</a>