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Parallel multigrid preconditioner for the cardiac bidomain model.

Rodrigo Weber dos Santos1, Gernot Plank, Steffen Bauer

  • 1Department of Biosignals, Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, D-10587 Berlin, Germany. rodrigo.weber@ptb.de

IEEE Transactions on Bio-Medical Engineering
|November 13, 2004
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Summary
This summary is machine-generated.

A new parallel multigrid (MG) preconditioner significantly speeds up cardiac electrical activity simulations by efficiently solving the elliptic part of the bidomain equations, offering a better speed-memory tradeoff.

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Area of Science:

  • Computational biology
  • Biomedical engineering
  • Numerical analysis

Background:

  • Bidomain equations are crucial for simulating cardiac electrical activity.
  • Current methods are computationally expensive, limiting model size.
  • The elliptic portion presents a significant computational bottleneck.

Purpose of the Study:

  • To find more efficient methods for solving the elliptic part of bidomain equations.
  • To evaluate a parallel multigrid (MG) preconditioner for conjugate gradient solvers.
  • To compare MG performance against traditional incomplete LU (ILU) preconditioners.

Main Methods:

  • Operator splitting technique to decompose the bidomain equations.
  • Preconditioned conjugate gradient method for the elliptic equation.
  • Parallel implementation using the PETSc library on a distributed cluster.
  • Comparison of MG and ILU preconditioners, optimizing parameters for each.

Main Results:

  • MG solved the system in one-third the time of ILU.
  • MG required approximately 40% more memory than ILU.
  • Performance of MG was between iterative (slow, low memory) and direct (fast, high memory) solvers.
  • Results were validated for 2D and 3D simulations on up to 16 nodes.

Conclusions:

  • The parallel MG preconditioner offers an attractive speed-memory tradeoff.
  • MG is well-suited for accelerating the accurate simulation of cardiac electrical activity.
  • This method can potentially enable larger and more complex cardiac models.