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Journal of Scientific Computing

, Volume 60, Issue 1, pp 35–59 | Cite as

Lossy Compression in Optimal Control of Cardiac Defibrillation

  • S. GötschelEmail author
  • N. Chamakuri
  • K. Kunisch
  • M. Weiser
Article

Abstract

This paper presents efficient computational techniques for solving an optimization problem in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical currents injected at different spatial positions act as the control. Inexact Newton-CG methods are used, with reduced gradient computation by adjoint solves. In order to reduce the computational complexity, adaptive mesh refinement for state and adjoint equations is performed. To reduce the high storage and bandwidth demand imposed by adjoint gradient and Hessian-vector evaluations, a lossy compression technique for storing trajectory data is applied. An adaptive choice of quantization tolerance based on error estimates is developed in order to ensure convergence. The efficiency of the proposed approach is demonstrated on numerical examples.

Keywords

Monodomain model Defibrillation Optimal control  Newton-CG Trajectory storage Compression 

Mathematics Subject Classification (2010)

35K57 35Q92 49M15 65M60 68P30 94A29 

Notes

Acknowledgments

The authors gratefully acknowledge support by the Austrian Science Foundation (FWF) under SFB 032, “Mathematical Optimization and Applications in Biomedical Sciences”, the Austrian Academy of Sciences (ÖAW) and by the DFG Research Center Matheon, project F9.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. Götschel
    • 1
    Email author
  • N. Chamakuri
    • 2
  • K. Kunisch
    • 2
    • 3
  • M. Weiser
    • 1
  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Radon Institute for Computational and Applied MathematicsLinzAustria
  3. 3.Institute of Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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