TY - CHAP A1 - Zeilhofer, Hans-Florian A1 - Sader, Robert A1 - Apostolescu, Victor A1 - Hoffmann, Karl-Heinz A1 - Göbel, Martin A1 - Hege, Hans-Christian T1 - Die Bedeutung breitbandiger und leistungsfähiger Kommunikationsinfrastrukturen für die kraniomaxillofaziale Chirurgie - Möglichkeiten der netzbasierten Bildverarbeitung T2 - Bildverarbeitung für die Medizin 2000 (Abstract) Y1 - 2000 CY - München ER - TY - JOUR A1 - Göbel, Fritz A1 - Huynh, Ngoc Mai Monica A1 - Chegini, Fatemeh A1 - Pavarino, Luca A1 - Weiser, Martin A1 - Scacchi, Simone A1 - Anzt, Hartwig T1 - A BDDC Preconditioner for the Cardiac EMI Model in three Dimensions JF - SIAM J. Sci. Comput. N2 - We analyze a Balancing Domain Decomposition by Constraints (BDDC) preconditioner for the solution of three dimensional composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models like the Extracellular space, Membrane and Intracellular space (EMI) Model. These microscopic models are essential for the understanding of events in aging and structurally diseased hearts which macroscopic models relying on homogenized descriptions of the cardiac tissue, like Monodomain and Bidomain models, fail to adequately represent. The modeling of each individual cardiac cell results in discontinuous global solutions across cell boundaries, requiring the careful construction of dual and primal spaces for the BDDC preconditioner. We provide a scalable condition number bound for the precondition operator and validate the theoretical results with extensive numerical experiments. Y1 - 2025 ER -