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Comput."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The application motivating this work is related to the identification of deposits inside nuclear power plant steam generators using eddy-current probes. We consider a realistic experimental process that relies on the scan of a domain by sweeping along a tube axis a probe made out of coils, playing the role of the sources\/receivers. Solving the inverse shape problem associated with these measurements using a least squares method requires solutions to the eddy-current and the adjoint problems for a large number of right-hand sides at each gradient-descent iteration. Additional cost in the forward solver comes from the use of a potential formulation of the problem that has the advantage of being independent from the topology of the conductive media (that may vary during iterations). We use a level-set approach to avoid remeshing and handle unknown topologies. The crucial ingredient in our algorithm is an optimized way of handling high numbers of right-hand sides for iterative solvers of large-scale problems. We first benchmark various block Krylov methods, block GMRES, and block BGCRODR to test their effectiveness compared to their standard counterpart, i.e., GMRES and GCRODR. Then we propose for BGCRODR a new implementation for recycling information from previously generated Krylov bases that scales better than traditional approaches. This part is independent from the practical inverse problem at hand. The efficiency of the overall inversion procedure is finally demonstrated on realistic synthetic 3D examples.<\/jats:p>","DOI":"10.1137\/20m1382064","type":"journal-article","created":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T04:13:43Z","timestamp":1686543223000},"page":"B366-B389","source":"Crossref","is-referenced-by-count":3,"title":["Inversion of Eddy-Current Signals Using a Level-Set Method and Block Krylov Solvers"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5767-4100","authenticated-orcid":true,"given":"Lorenzo","family":"Audibert","sequence":"first","affiliation":[{"name":"PRISME, EDF R&D, 6 Quai Watier, 78400 Chatou, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hugo","family":"Girardon","sequence":"additional","affiliation":[{"name":"PRISME, EDF R&D, 6 Quai Watier, 78400 Chatou, France, and INRIA and Ecole Polytechnique, CMAP, Institut Polytechnique de Paris, 91128, Palaiseau, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Houssem","family":"Haddar","sequence":"additional","affiliation":[{"name":"INRIA and Ecole Polytechnique, CMAP, Institut Polytechnique de Paris, 91128, Palaiseau, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Jolivet","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, CNRS, LIP6, 75252 Paris Cedex 05, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,12]]},"reference":[{"key":"ref1","first-page":"59","volume":"34","author":"Allaire G.","year":"2005","journal-title":"Control Cybernet."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899358194"},{"key":"ref3","unstructured":"S. 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