Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart

Comput Methods Biomech Biomed Engin. 2002 Dec;5(6):397-409. doi: 10.1080/1025584021000025023.

Abstract

The electrical activity of the heart may be modeled with a system of partial differential equations (PDEs) known as the bidomain model. Computer simulations based on these equations may become a helpful tool to understand the relationship between changes in the electrical field and various heart diseases. Because of the rapid variations in the electrical field, sufficiently accurate simulations require a fine-scale discretization of the equations. For realistic geometries this leads to a large number of grid points and consequently large linear systems to be solved for each time step. In this paper, we present a fully coupled discretization of the bidomain model, leading to a block structured linear system. We take advantage of the block structure to construct an efficient preconditioner for the linear system, by combining multigrid with an operator splitting technique.

Publication types

  • Evaluation Study
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials / physiology*
  • Anatomy, Cross-Sectional
  • Anisotropy
  • Body Surface Potential Mapping / methods*
  • Computer Simulation
  • Computing Methodologies
  • Electric Conductivity
  • Electromagnetic Fields
  • Heart / physiology*
  • Heart Conduction System / physiology
  • Humans
  • Linear Models
  • Models, Cardiovascular*
  • Muscle Cells / physiology*
  • Quality Control
  • Thorax / physiology