Physics aware programming paradigm: approach and evaluation

ABSTRACT

Large scale scientific applications generally experience different execution phases at runtime and each phase has different computational and communication requirements. An optimal solution or numerical scheme for one execution phase might not be appropriate for the next phase of the application execution. In this paper we present Physics Aware Programming (PAP) paradigm that supports dynamic changes of the application solution if it optimizes the application performance at runtime. In the PAP approach, the application execution state is periodically monitored and analyzed to identify its current execution phase (state). For each change in the application execution phase, we will exploit the spatial and temporal attributes of the application physics to select the numerical algorithms/solvers that optimize its performance. We have applied our approach to a Ten-Tusscher's model of human ventricular epicardia myocyte paced at a varied cycle length (1000 to 50 ms). At runtime, we recognize the current phase of the heart simulation and based on the detected phase, we adopt the simulation Δt that maximizes the performance and maintains the required accuracy. Our experimental results show that we can achieve a speedup of three orders of magnitude while maintaining the required accuracy.

REFERENCES

• 1: Gerhard Zumbusch, "Parallel Multilevel Methods: Adaptive Mesh Refinement and Loadbalancing," Teubner, 2003.
• 2: J. H. Ferziger, "Numerical Methods for Engineering Application," John Wiley & Sons, Inc. 1998.
• 3: W. Press, S. Teukolsky, W. Vetterling and B. Flannery, "Numerical Recipes in Fortran 77," Cambridge University Press, 1992.
• 4: George Hornberger and Patricia Wiberg, "Numerical Methods in the Hydrological Sciences", American Geophysical Union, 2005.
• 5: O. C. Zienkiewicz, The Finite Element Method, 3rd.Ed. MacGRAW-HILL Book Company (UK) Ltd. 1977.
• 6: P. Bochev, M. Gunzburger and R. Lehoucq, "On stabilized finited element methods for transient problems with varying time scales", European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004.
• 7: S. Liu, M. Rodgers, Q. Wang and L. Keer, "A Fast and Effective Method for Transient Thermoelastic Displacement Analyses", Journal of Tribology -- July 2001 -- Volume 123, Issue 3, pp. 479--485.
• 8: Touheed, N; Selwood, P; Jimack, P K; Berzins, M. Parallel dynamic load-balancing for the solution of transient CFD problems using adaptive tetrahedral meshes in: Emerson D R, Ecer, A, Periaux, J, Satofuka, N & Fox, P (editors Parallel Computational Fluid Dynamics - Recent Developments and Advances Using Parallel Computers, pp. 81--88 Elsevier Science. 1998.
• 9: Goodyer, C; Fairlie, R; Berzins, M; Scales, L. An in-depth investigation of the multigrid approach for steady and transient EHL problems in: Dowson, D (editors) Thinning Films and Tribological Interfaces - Proceedings of the 26th Leeds-Lyon Symposium, pp. 95--102 Elsevier Science. 1999.
• 10: J. C. Tannehill, D. A. Anderson, R. H. Pletcher. Computational fluid mechanics and heat transfer, 2nd. Edition, Taylor & Francis.
• 11: L. Eldén. Numerical Solution of the Sideways Heat Equation. In Inverse Problems in Diffusion Processes. Proceedings in Applied Mathematics, ed. H. Engl and W. Rundell, SIAM, Philadelphia 1995.
• 12: Paul Duchateau and David Zachmann, Applied Partial Differential Equations, Dover Publications, Inc. 1989.
• 13: K.H.W.J. ten Tusscher et al., "A model for human ventricular tissue," American journal of physiology. Heart and circulatory physiology, vol. 286, Apr. 2004, pp. H1573--89.
• 14: Ian H. Witten , Eibe Frank, Data Mining: Practical Machine Learning Tools and Techniques, Second Edition (Morgan Kaufmann Series in Data Management Systems), Morgan Kaufmann Publishers Inc., San Francisco, CA, 2005
• 15: Pieter Adriaans and Dolf Zantinge, Introduction to Data Mining and Knowledge Discovery, Third Edition (New York: Addison Wesley, 1996).
• 16: Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications, Inc. 1993.
• 17: R. Plonsey and R.C. Barr, Bioelectricity: A Quantitative Approach, Springer, 2007.
• 18: C.E. Clancy, Z.I. Zhu, and Y. Rudy, "Pharmacogenetics and anti-arrhythmic drug therapy: a theoretical investigation," American journal of physiology. Heart and circulatory physiology, vol. 292, Jan. 2007, pp. H66--75.
• 19: K .H.W.J. ten Tusscher and A.V. Panfilov, "Alternans and spiral breakup in a human ventricular tissue model," American journal of physiology. Heart and circulatory physiology, vol. 291, Sep. 2006, pp. H1088--100.
• 20: P.C. Viswanathan and Y. Rudy, "Cellular Arrhythmogenic Effects of Congenital and Acquired Long-QT Syndrome in the Heterogeneous Myocardium," Circulation, vol. 101, Mar. 2000, pp. 1192--1198.
• 21: J. Sundnes et al., Computing the Electrical Activity in the Heart, Springer, 2006.
• 22: K.H.W.J. Ten Tusscher and A.V. Panfilov, "Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions," Physics in medicine and biology, vol. 51, Dec. 2006, pp. 6141---56.

INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.3 LIFE AND MEDICAL SCIENCES
      Subjects: Medical information systems

General Terms:
Algorithms, Design, Experimentation, Performance, Theory

Keywords:
autonomic computing, data mining, heart simulation, physics aware programming paradigm