Related papers: A dual adaptive explicit time integration algorith…
We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of…
Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to the need of capturing fine-scale processes and to the…
We propose a novel family of asymptotically stable, implicit-explicit, adaptive, time integration method (denoted with the $\theta$-method) for the solution of the fractional advection-diffusion-reaction (FADR) equations. This family of…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the…
Implicit time integration schemes are widely used in computational fluid dynamics numerical codes to speed-up computations. Indeed, implicit schemes usually allow for less stringent time-step stability constraints than their explicit…
The pressure-correction method is a well established approach for simulating unsteady, incompressible fluids. It is well-known that implicit discretization of the time derivative in the momentum equation e.g. using a backward…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
In this study, we consider a system of degenerate reaction-diffusion equations, which govern the electric activity in the heart with a diffusion term modeling the potential in the surrounding tissue and the nonlinear ionic model proposed by…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent…
The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated pattern formation in the developing animal embryo. In this…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…
Clinical oriented applications of computational electrocardiology require efficient and reliable identification of patient-specific parameters of mathematical models based on available measures. In particular, the estimation of cardiac…
For time-dependent problems with high-contrast multiscale coefficients, the time step size for explicit methods is affected by the magnitude of the coefficient parameter. With a suitable construction of multiscale space, one can achieve a…
Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
We analyze an advection-diffusion-reaction problem with non-homogeneous boundary conditions that models the chromatography process, a vital stage in bioseparation. We prove stability and error estimates for both constant and affine…