Related papers: A dual adaptive explicit time integration algorith…
This work deals with the numerical solution of the monodomain and bidomain models of electrical activity of myocardial tissue. The bidomain model is a system consisting of a possibly degenerate parabolic PDE coupled with an elliptic PDE for…
The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic reaction diffusion equations coupled with an ODE system. Its…
For plane-wave and many-spiral states of the experimentally based Luo-Rudy 1 model of heart tissue in large (8 cm square) domains, we show that an explicit space-time-adaptive time-integration algorithm can achieve an order of magnitude…
This work aims at presenting a Discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
The bidomain system of degenerate reaction-diffusion equations is a well-established spatial model of electrical activity in cardiac tissue, with "reaction" linked to the cellular action potential and "diffusion" representing current flow…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The problem is discretized using $P_1$ finite elements in space,…
Computational models are increasingly used for diagnosis and treatment of cardiovascular disease. To provide a quantitative hemodynamic understanding that can be effectively used in the clinic, it is crucial to quantify the variability in…
The numerical tools to simulate the bidomain model in cardiac electrophysiology are constantly developing due to the great clinical interest and scientific advances in mathematical models and computational power. The bidomain model consists…
Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature,…
The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…
The time domain analysis of eddy current problems often requires the simulation of long time intervals, e.g. until a steady state is reached. Fast-switching excitations e.g. in pulsedwidth modulated signals require in addition very small…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
Electrical conduction among cardiac tissue is commonly modeled with partial differential equations, i.e., reaction-diffusion equation, where the reaction term describes cellular stimulation and diffusion term describes electrical…
This work proposes a stabilized space--time method for the monodomain equation coupled with the Rogers--McCulloch ionic model, which is widely used to simulate electrophysiological wave propagation in the cardiac tissue. By extending the…
Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their…
This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions,…