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Accelerating large cardiac bidomain simulations by arnoldi preconditioning.

Makarand Deo1, Steffen Bauer, Gernot Plank

  • 1Calgary Univ., Alta. mdeo@ucalgary.ca

Conference Proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference
|October 20, 2007
PubMed
Summary

This study introduces an efficient Arnoldi-based preconditioner for conjugate gradient (CG) methods, significantly speeding up cardiac bidomain simulations. The new method (A-PCG) offers faster approximate solutions compared to traditional incomplete LU (ILU) preconditioning.

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Area of Science:

  • Computational Biology
  • Numerical Analysis
  • Biomedical Engineering

Background:

  • Cardiac bidomain simulations require solving large, sparse linear systems (Ax=b).
  • These simulations are computationally intensive, demanding efficient solvers for tractability.
  • Existing methods like incomplete LU (ILU) preconditioning have limitations.

Purpose of the Study:

  • To introduce and evaluate an efficient preconditioner for the conjugate gradient (CG) method tailored for cardiac bidomain simulations.
  • To compare the performance of the proposed Arnoldi-based preconditioner (A-PCG) against established methods like ILU preconditioning.
  • To explore strategies for reducing computational demands, including memory and runtime.

Main Methods:

  • Development and application of an Arnoldi-based preconditioner (A-PCG) for system order reduction.
  • Solving large-scale linear systems from finite element method (FEM) cardiac bidomain simulations using A-PCG.
  • Comparative analysis of A-PCG performance against incomplete LU (ILU) preconditioning.
  • Investigation of cascaded preconditioner strategies, combining A-PCG with successive overrelaxation (SOR).

Main Results:

  • The A-PCG method significantly accelerates the estimation of approximate solutions, often within a single iteration, outperforming ILU.
  • The A-PCG method demonstrates considerable speedups for time-evolving cardiac bidomain systems.
  • Cascaded preconditioner approaches, using A-PCG followed by SOR, effectively refine solutions to desired accuracy while managing computational costs.
  • Memory requirements for A-PCG are between direct LU decomposition and ILU methods.

Conclusions:

  • The Arnoldi-based preconditioner (A-PCG) offers a computationally efficient solution for large-scale linear systems in cardiac bidomain simulations.
  • A-PCG provides substantial speedups, making complex cardiac modeling more tractable.
  • Cascaded preconditioner strategies present a viable approach to balance speed and accuracy in these demanding simulations.