地点：行健楼学术活动室526
邀请人：王锋
Abstract: Scalable preconditioners are constructed and analyzed for the iterative solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. These models lead to large-scale ill-conditioned discrete systems which have discontinuous global solutions across cells (subdomains) boundaries. A scalable convergence rate bound is proved for dual-primal cell-by-cell preconditioned operators. Numerical tests validate this bound and investigate its dependence on the discretization parameters [1]. Possible extensions of this work include the study of Newton-Krylov and Quasi-Newton preconditioned solvers [3,4] to implicit discretizations of cell-by-cell cardiac models.
References:
[1] Huynh, N. M. M., Chegini, F., Pavarino, L. F., Weiser, M., & Scacchi, S. Convergence analysis of BDDC preconditioners for composite DG discretizations of the cardiac cell-by-cell model. SIAM Journal on Scientific Computing, 45(6), A2836-A2857, 2023.
[2] Franzone, P. C., Pavarino, L. F., & Scacchi, S. Mathematical cardiac electrophysiology. Springer. 2014
[3] Yi Jiang, Zhengzheng Yan, Xinhong Wang, Rongliang Chen, Xiao-Chuan Cai. A highly parallel algorithm for simulating the elastodynamics of a patient-specific human heart with four chambers using a heterogeneous hyperelastic model. Journal of Computational Physics, 508, (2024): 113027.
[4] Huynh, Ngoc Mai Monica, Luca F. Pavarino, Simone Scacchi. Parallel Newton--Krylov BDDC and FETI-DP Deluxe Solvers for Implicit Time discretizations of the Cardiac Bidomain Equations. SIAM Journal on Scientific Computing 44.2 (2022): B224-B249.
