Sharp Boundary Electrocardiac Simulations

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Physiological flow (92C35) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Finite volume methods for boundary value problems involving PDEs (65N08)

Cites Work

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A two-current model for the dynamics of cardiac membrane
Exploring anodal and cathodal make and break cardiac excitation mechanisms in a 3D anisotrop\-ic bidomain model
A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions
An embedded boundary method for elliptic and parabolic problems with interfaces and application to multi-material systems with phase transitions
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Numerical analysis of blood flow in the heart
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
An overview of the immersed interface method and its applications
A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers
A Cartesian grid embedded boundary method for the heat equation and Poisson's equation in three dimensions
Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation
IMMERSED BOUNDARY METHODS
Spectral Methods for Partial Differential Equations in Irregular Domains: The Spectral Smoothed Boundary Method
Sharp Interface and Voltage Conservation in the Phase Field Method: Application to Cardiac Electrophysiology
Arrhythmogenesis in the heart: Multiscale modeling of the effects of defibrillation shocks and the role of electrophysiological heterogeneity
Adaptive h‐refinement on 3D unstructured grids for transient problems
Uniformly Accurate Finite Difference Schemes forp-Refinement
Preconditioning Techniques for the Bidomain Equations
Application of high‐order quadrature rules to time‐domain boundary element analysis of viscoelasticity
On the Construction and Comparison of Difference Schemes
Modeling wave propagation in realistic heart geometries using the phase-field method
A Cartesian grid embedded boundary method for the heat equation on irregular domains

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