Munteanu, M., Pavarino, L.F., Scacchi, S.: A scalable Newton–Krylov–Schwarz method for the Bidomain reaction-diffusion system. Munteanu, M., Pavarino, L.F.: Decoupled Schwarz algorithms for implicit discretization of nonlinear Monodomain and Bidomain systems. Mardal, K.-A., Nielsen, B.F., Cai, X., Tveito, A.: An order optimal solver for the discretized bidomain equations. Luo, C., Rudy, Y.: A model of the ventricular cardiac action potential: depolarization, repolarization, and their interaction. Hwang, F.-N., Cai, X.-C.: A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms. (eds.) Complex Systems in Biomedicine, pp. 14 (6), 883–911 (2004)Ĭolli Franzone, P., Pavarino, L.F., Savaré G.: Computational electrocardiology: mathematical and numerical modeling. 24 (1), 183–200 (2002)Ĭolli Franzone, P., Pavarino, L.F.: A parallel solver for reaction-diffusion systems in computational electrocardiology. ANL-95/11 - Revision 2.1.5, Argonne National Laboratory (2002)Ĭai, X.-C., Keyes, D.: Nonlinearly preconditioned inexact Newton algorithms. This theoretical result is confirmed by several parallel simulations employing up to more than 2,000 processors for scaled and standard speedup tests in three dimensions.īalay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M., Curfman McInnes, L., Smith, B.F., Zhang, H.: PETSc Users Manual. A convergence rate estimate is proved for the resulting preconditioned operator, showing that its condition number is independent of the number of subdomains (scalability) and bounded by the ratio of the subdomains characteristic size and the overlap size. The Jacobian update during the Newton iteration is solved by a Krylov method employing a two-level overlapping Schwarz preconditioner. The proposed NKS Bidomain solver employs an outer inexact Newton iteration to solve the nonlinear finite element system originating at each time step of the implicit discretization. This multiscale system describes the bioelectrical activity of the heart by coupling two degenerate parabolic equations with several ordinary differential equations at each point in space. A two-level Newton–Krylov–Schwarz (NKS) solver is constructed and analyzed for implicit time discretizations of the Bidomain reaction-diffusion system.
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