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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

Stimulus protocol determines the most computationally efficient preconditioner for the bidomain equations.

Miguel O Bernabeu1, Pras Pathmanathan, Joe Pitt-Francis

  • 1Oxford University Computing Laboratory, Oxford, UK. miguel.bernabeu@comlab.ox.ac.uk

IEEE Transactions on Bio-Medical Engineering
|September 30, 2010
PubMed
Summary
This summary is machine-generated.

Optimizing preconditioners for solving bidomain equations in cardiac electrophysiology is crucial. For intracellular stimulation, incomplete LU factorization is effective, but extracellular stimulation requires structured preconditioners for faster, mesh-independent results.

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Area of Science:

  • Cardiac electrophysiology
  • Computational modeling
  • Biomedical engineering

Background:

  • The bidomain equations are essential for simulating cardiac electrical activity.
  • Solving these equations involves large, sparse linear systems, often using the conjugate gradient method.
  • Preconditioning is vital for efficient numerical solution.

Purpose of the Study:

  • To identify optimal preconditioning strategies for the bidomain equations.
  • To analyze the impact of stimulus protocol and mesh geometry on preconditioning performance.
  • To evaluate mesh-dependence properties of various preconditioning techniques.

Main Methods:

  • Finite element discretization of the bidomain equations.
  • Application of the conjugate gradient algorithm with different preconditioners.
  • Systematic study of preconditioning techniques, including incomplete LU factorization and structured preconditioners.
  • Analysis of mesh-dependence and computational efficiency.

Main Results:

  • Incomplete LU factorization is suitable for intracellular stimulation in typical cardiac geometries.
  • Preconditioners exploiting system structure are superior for extracellular stimulation, minimizing execution time.
  • Structured preconditioners ensure mesh-independent convergence for extracellular shocks.

Conclusions:

  • The choice of preconditioner for bidomain equation solvers depends critically on the stimulus protocol.
  • For extracellular stimulation, structured preconditioners offer significant advantages in computational efficiency and robustness.
  • Optimized preconditioning is key to accurate and efficient cardiac electrophysiology simulations.