5069
2014
eng
reportzib
0
--
2014-06-20
--
Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation
We investigate spectral deferred correction (SDC) methods for time stepping
and their interplay with spatio-temporal adaptivity, applied to the solution
of the cardiac electro-mechanical coupling model. This model consists
of the Monodomain equations, a reaction-diffusion system modeling the cardiac
bioelectrical activity, coupled with a quasi-static mechanical model describing
the contraction and relaxation of the cardiac muscle. The numerical
approximation of the cardiac electro-mechanical coupling is a challenging
multiphysics problem, because it exhibits very different spatial and temporal
scales. Therefore, spatio-temporal adaptivity is a promising approach
to reduce the computational complexity. SDC methods are simple iterative
methods for solving collocation systems. We exploit their flexibility for combining
them in various ways with spatio-temporal adaptivity. The accuracy
and computational complexity of the resulting methods are studied on some
numerical examples.
1438-0064
urn:nbn:de:0297-zib-50695
accepted for publication
Martin Weiser
Martin Weiser
Simone Scacchi
ZIB-Report
14-22
Mesh generation and refinement
Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Spectral, collocation and related methods
Medical applications (general)
Numerical Mathematics
Computational Medicine
Weiser, Martin
ZIB-Cardio
ZIB-Kaskade7
https://opus4.kobv.de/opus4-zib/files/5069/weiser_ecmi14_ZIBReport.pdf
5198
2017
eng
321
328
conferenceobject
Springer
0
--
--
--
Spectral Deferred Correction methods for adaptive electro-mechanical coupling in cardiac simulation
We investigate spectral deferred correction (SDC) methods for time stepping
and their interplay with spatio-temporal adaptivity, applied to the solution
of the cardiac electro-mechanical coupling model. This model consists
of the Monodomain equations, a reaction-diffusion system modeling the cardiac
bioelectrical activity, coupled with a quasi-static mechanical model describing
the contraction and relaxation of the cardiac muscle. The numerical
approximation of the cardiac electro-mechanical coupling is a challenging
multiphysics problem, because it exhibits very different spatial and temporal
scales. Therefore, spatio-temporal adaptivity is a promising approach
to reduce the computational complexity. SDC methods are simple iterative
methods for solving collocation systems. We exploit their flexibility for combining
them in various ways with spatio-temporal adaptivity. The accuracy
and computational complexity of the resulting methods are studied on some
numerical examples.
G. Russo et al.(eds.) Progress in Industrial Mathematics at ECMI 2014
10.1007/978-3-319-23413-7_42
yes
urn:nbn:de:0297-zib-50695
Martin Weiser
Martin Weiser
Simone Scacchi
Numerical Mathematics
Computational Medicine
Weiser, Martin
ZIB-Cardio
ZIB-Kaskade7
8930
2023
eng
A2836
A2857
6
45
article
0
--
--
--
Convergence analysis of BDDC preconditioners for hybrid DG discretizations of the cardiac cell-by-cell model
A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of hybrid Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential equations arising in cardiac cell-by-cell models. The latter are different from the classical Bidomain and Monodomain cardiac models based on homogenized descriptions of the cardiac tissue at the macroscopic level, and therefore they allow the representation of individual cardiac cells, cell aggregates, damaged tissues and nonuniform distributions of ion channels on the cell membrane. The resulting discrete cell-by-cell models have discontinuous global solutions across the cell boundaries, hence the proposed BDDC preconditioner is based on appropriate dual and primal spaces with additional constraints which transfer information between cells (subdomains) without influencing the overall discontinuity of the global solution. A scalable convergence rate bound is proved for the resulting BDDC cell-by-cell preconditioned operator, while numerical tests validate this bound and investigate its dependence on the discretization parameters.
SIAM Journal on Scientific Computing
2212.12295
yes
publish
2023-08-23
Ngoc Huynh
Martin Weiser
Fatemeh Chegini
Luca Pavarino
Martin Weiser
Simone Scacchi
Weiser, Martin
ZIB-Cardio
ZIB-Kaskade7
Modeling and Simulation of Complex Processes
Chegini, Fatemeh
9334
2023
eng
conferenceobject
0
--
--
--
Efficient numerical methods for simulating cardiac electrophysiology with cellular resolution
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.
10th Int. Conf. Computational Methods for Coupled Problems in Science and Engineering 2023
10.23967/c.coupled.2023.004
https://www.scipedia.com/public/2023f
no
publish
false
true
Creative Commons - CC BY-NC-SA - Namensnennung - Nicht kommerziell - Weitergabe unter gleichen Bedingungen 4.0 International
Fatemeh Chegini
Martin Weiser
Algiane Froehly
Ngoc Mai Monica Huynh
Luca Pavarino
Mark Potse
Simone Scacchi
Martin Weiser
Numerical Mathematics
Weiser, Martin
ZIB-Cardio
Modeling and Simulation of Complex Processes
Chegini, Fatemeh