相关论文: Preconditioning the bidomain model with almost lin…

We present a loosely coupled scheme for the numerical simulation of the cardiac electro-fluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the…

To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…

We propose a matrix-free solver for the numerical solution of the cardiac electrophysiology model consisting of the monodomain nonlinear reaction-diffusion equation coupled with a system of ordinary differential equations for the ionic…

In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [45]. The discretization is proved to be well-posed with respect to the physical and discretization parameters, and…

The study of pathological cardiac conditions such as arrhythmias, a major cause of mortality in heart failure, is becoming increasingly informed by computational simulation, numerically modelling the governing equations. This can provide…

We study a preconditioner for a Hermitian positive definite linear system, which is obtained as the solution of a matrix nearness problem based on the Bregman log determinant divergence. The preconditioner is of the form of a Hermitian…

This paper presents a finite-volume method, together with fully adaptive multi-resolution scheme to obtain spatial adaptation, and a Runge-Kutta-Fehlberg scheme with a local time-varying step to obtain temporal adaptation, to solve…

In this work, we study the convergence and performance of nonlinear solvers for the Bidomain equations after decoupling the ordinary and partial differential equations of the cardiac system. Firstly, we provide a rigorous proof of the…

The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric…

This paper is about partitioning in parallel and distributed simulation. That means decomposing the simulation model into a numberof components and to properly allocate them on the execution units. An adaptive solution based on…

There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\Omega \subset \R^d$ containing a set of small subdomains or interior…

We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…

The Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the…

Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…

This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…

A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number…

The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…

In this study we derive the Finite element apriori error estimate for the monodomain cardiac electric model in conjunction with the generic form for a class of nonlinear ionic models. The analysis establishes a $o(h^2+k)$ space-time…

We develop a numerical Brillouin-zone integration scheme for real-time propagation of electronic systems with time-dependent density functional theory. This scheme is based on the decomposition of a large simulation into a set of small…