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Memory footprint reduction for the FFT-based volume integral equation method via tensor decompositions [article]

Ilias I. Giannakopoulos, Athanasios G. Polimeridis Skoltech Center for Computational Data-Intensive Science and Engineering, Skolkovo Institute of Science and Technology, Moscow, Russia
<span title="2019-07-16">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a method of memory footprint reduction for FFT-based, electromagnetic (EM) volume integral equation (VIE) formulations.  ...  For these simulations we report an order of magnitude acceleration over standard techniques.  ...  , for the case of a highly inhomogeneous realistic human head model.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.00484v3">arXiv:1811.00484v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h7ajj6zcovfcva5jgfq4gsshwq">fatcat:h7ajj6zcovfcva5jgfq4gsshwq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200928121821/https://arxiv.org/pdf/1811.00484v2.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f8/73/f8730de130e960f26b53c8077cc1d850c3ce4d1d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.00484v3" 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>

Discrete Helmholtz Decomposition for Electric Current Volume Integral Equation Formulation

Johannes Markkanen
<span title="">2014</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yixmmnv7u5hzfmuufaamg2cm2u" style="color: black;">IEEE Transactions on Antennas and Propagation</a> </i> &nbsp;
We construct discrete decomposition operators, and use them as a preconditioner for the electric current volume integral equation.  ...  A volume integral equation formulation for the equivalent current is investigated by decomposing the L2conforming unknown current into orthogonal functions.  ...  As an example Fig. 3 shows computational times for the FFT-accelerated matrix-vector multiplication y = Ax (one iteration step in FFT-JVIE solver), projectionsP s y andP i y when the pseudo-inversesS  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tap.2014.2364614">doi:10.1109/tap.2014.2364614</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kp57ktr6ujdnzdttwnqc6zzlua">fatcat:kp57ktr6ujdnzdttwnqc6zzlua</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922230906/https://helda.helsinki.fi/bitstream/handle/10138/152742/TAP2364614.pdf?sequence=1" 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/8f/c7/8fc7dafd6b40c97c336d0b66629da4825b7bacd2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tap.2014.2364614"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications [article]

Ilias I. Giannakopoulos, Georgy D. Guryev, Jose E. C. Serralles, Ioannis P. Georgakis, Luca Daniel, Jacob K. White, Riccardo Lattanzi
<span title="2021-06-02">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
VSIE methods are used for electromagnetic analysis in magnetic resonance imaging (MRI) applications, for which the coupling matrix models the interactions between the coil and the body.  ...  Our method can work in tandem with the adaptive cross approximation technique to provide fast solutions of VSIE problems.  ...  Polimeridis et al., “Stable FFT-JVIE solvers for fast analysis of highly inhomogeneous dielectric objects,” Journal of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.06393v2">arXiv:2103.06393v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gmocqvxzt5g47fxkaankb33b2a">fatcat:gmocqvxzt5g47fxkaankb33b2a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210605114943/https://arxiv.org/pdf/2103.06393v2.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/cd/cd/cdcd90ed5108b7b7808594da4cd751a9986ac280.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.06393v2" 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>