Abstract
We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes are treated. A short description is given of the 3D DDFV meshes and of some of the associated discrete calculus tools. Several numerical tests are presented.
Highlights
We consider the heart of a living organism that occupies a fixed domain Ω, which is assumed to be a bounded open subset of R3 with Lipschitz boundary ∂Ω
Our study can be considered as a theoretical and numerical validation of the discrete duality finite volume (DDFV) discretisation strategy for the bidomain model. For both a fully timeimplicit scheme and a linearised time-implicit scheme, we prove convergence of different DDFV discretisations to the unique solution of the bidomain model (1)
We prove the convergence of each of these schemes, using only general properties of DDFV approximations; but the main focus is on scheme (B), which construction is detailed
Summary
We consider the heart of a living organism that occupies a fixed domain Ω, which is assumed to be a bounded open subset of R3 with Lipschitz boundary ∂Ω. 2our notation follows [7]; a slightly different viewpoint was used in [4, 5, 2, 3], where the homogeneous Dirichlet boundary data were included into the definition of the space RT 0 of discrete functions defined on the control volumes adjacent to ΓD ≡ ∂Ω. In this paper a standard finite volume divergence operator is defined and the definition of a gradient operator is replaced by a dual property (of discrete Green Gauss formula type) together with the definition of a consistent scalar product. A major difference is that, the discrete divergence need not be computed in practice, it has a simple and natural definition (it is a flux balance as usual for finite volume schemes), whereas in the case of Mimetic schemes only a dual and abstract definition of the gradient is provided.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
