Related papers: A dual adaptive explicit time integration algorith…
The numerical simulation of cardiac electrophysiology is a highly challenging problem in scientific computing. The Bidomain system is the most complete mathematical model of cardiac bioelectrical activity. It consists of an elliptic and a…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the…
We prove the existence and the uniqueness of a solution for a modified bidomain model, describing the electrical behaviour of the cardiac tissue in pathological situations. The leading idea is to reduce the problem to an abstract parabolic…
A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…
A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac Bidomain model, describing the propagation of the electric impulse in the cardiac tissue.…
This paper develops a strong computational approach to simulate a three-dimensional nonlinear radiation-conduction model in optically thick media, subject to suitable initial and boundary conditions. The space derivatives are approximated…
In this paper, we find relations between the ionic parameters and the diffusion parameters which are sufficient to ensure the existence of a periodic solution for a well-known monodomain model in a weak sense. We make use of the method of…
Objective: The bidomain model and the finite element method are an established standard to mathematically describe cardiac electrophysiology, but are both suboptimal choices for fast and large-scale simulations due to high computational…
Solving partial or ordinary differential equation models in cardiac electrophysiology is a computationally demanding task, particularly when high-resolution meshes are required to capture the complex dynamics of the heart. Moreover, in…
The primary goal of this paper is to characterize solutions to coupled reaction-diffusion systems. Indeed, we use operators theory to show that under suitable assumptions, then the solutions to the reaction-diffusion equations exist. As…
A combination of a steady-state preserving operator splitting method and a semi-implicit integration scheme is proposed for efficient time stepping in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical…
We analyze a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs…
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators applied to stiff diffusion problems. In this paper, we provide…
Many multiscale problems have a high contrast, which is expressed as a very large ratio between the media properties. The contrast is known to introduce many challenges in the design of multiscale methods and domain decomposition…
In this paper we continue our work on adaptive timestep control for weakly non- stationary problems. The core of the method is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. The…
We present a simulation algorithm that accurately propagates a molecule pair using large time steps without the need to invoke the full exact analytical solutions of the Smoluchowski diffusion equation. Because the proposed method only uses…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be…