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    <publishedYear>2025</publishedYear>
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    <language>eng</language>
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    <title language="eng">A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions</title>
    <abstract language="eng">We analyze a Balancing Domain Decomposition by Constraints (BDDC)&#13;
preconditioner for the solution of three dimensional composite Discontinuous&#13;
Galerkin discretizations of reaction-diffusion systems of ordinary and partial&#13;
differential equations arising in cardiac cell-by-cell models like the&#13;
Extracellular space, Membrane and Intracellular space (EMI) Model. These&#13;
microscopic models are essential for the understanding of events in aging and&#13;
structurally diseased hearts which macroscopic models relying on homogenized&#13;
descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail&#13;
to adequately represent. The modeling of each individual cardiac cell results&#13;
in discontinuous global solutions across cell boundaries, requiring the careful&#13;
construction of dual and primal spaces for the BDDC preconditioner. We provide&#13;
a scalable condition number bound for the precondition operator and validate&#13;
the theoretical results with extensive numerical experiments.</abstract>
    <parentTitle language="eng">SIAM J. Sci. Comput.</parentTitle>
    <identifier type="arxiv">2502.07722</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="AcceptedDate">2025-11-03</enrichment>
    <author>Fritz Göbel</author>
    <submitter>Martin Weiser</submitter>
    <author>Ngoc Mai Monica Huynh</author>
    <author>Fatemeh Chegini</author>
    <author>Luca Pavarino</author>
    <author>Martin Weiser</author>
    <author>Simone Scacchi</author>
    <author>Hartwig Anzt</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ZIB-Cardio">ZIB-Cardio</collection>
    <collection role="projects" number="ZIB-Kaskade7">ZIB-Kaskade7</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="Chegini">Chegini, Fatemeh</collection>
  </doc>
  <doc>
    <id>9334</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
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    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution</title>
    <abstract language="eng">The cardiac extracellular-membrane-intracellular (EMI) model enables the precise geometrical representation and resolution of aggregates of individual myocytes. As a result, it not only yields more accurate simulations of cardiac excitation compared to homogenized models but also presents the challenge of solving much larger problems. In this paper, we introduce recent advancements in three key areas: (i) the creation of artificial, yet realistic grids, (ii) efficient higher-order time stepping achieved by combining low-overhead spatial adaptivity on the algebraic level with progressive spectral deferred correction methods, and (iii) substructuring domain decomposition preconditioners tailored to address the complexities of heterogeneous problem structures. The efficiency gains of these proposed methods are demonstrated through numerical results on cardiac meshes of different sizes.</abstract>
    <parentTitle language="eng">10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023</parentTitle>
    <identifier type="doi">10.23967/c.coupled.2023.004</identifier>
    <identifier type="url">https://www.scipedia.com/public/2023f</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">true</enrichment>
    <licence>Creative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell -  Weitergabe unter gleichen Bedingungen 4.0 International</licence>
    <author>Fatemeh Chegini</author>
    <submitter>Martin Weiser</submitter>
    <author>Algiane Froehly</author>
    <author>Ngoc Mai Monica Huynh</author>
    <author>Luca Pavarino</author>
    <author>Mark Potse</author>
    <author>Simone Scacchi</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ZIB-Cardio">ZIB-Cardio</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="persons" number="Chegini">Chegini, Fatemeh</collection>
  </doc>
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