Skip to main content

Scientific Computing - Why, What, How and What's Next

  • Chapter
  • First Online:
Simula Research Laboratory

Abstract

Problems in science and engineering have traditionally been solved by a combination of theory and experiment. In many branches of science, the theories are based on mathematical models, usually in the form of equations describing the physical world. By formulating and solving these equations, one can understand and predict the physical world. The theories are constructed from or validated by physical experiments under controlled conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. FEniCS software collection. http://www.fenics.org.

  2. Diffpack software package. http://www.diffpack.com.

  3. H. P. Langtangen. Python Scripting for Computational Science. Texts in Computational Science and Engineering. Springer, third edition, 2009.

    Google Scholar 

  4. H. P. Langtangen. Computational Partial Differential Equations—Numerical Methods and Diffpack Programming. Texts in Computational Science and Engineering. Springer, 2nd edition, 2003.

    Google Scholar 

  5. J. Sundnes, G. Lines, X. Cai, B. F. Nielsen, K. A. Mardal, and A. Tveito. Computing the electrical activity in the heart. Monographs in Computational Science and Engineering. Springer, 2006.

    Google Scholar 

  6. X. Cai, H. P. Langtangen, and H. Moe. On the performance of the Python programming language for serial and parallel scientific computations. Scientific Programming, 13(1):31–56, 2005.

    Google Scholar 

  7. H. P. Langtangen and X. Cai. On the efficiency of Python for high-performance computing: A case study involving stencil updates for partial differential equations. Modeling, Simulation and Optimization of Complex Processes, pages 337–358. Springer, 2008.

    Google Scholar 

  8. H. P. Langtangen and A. Tveito, editors. Advanced Topics in Computational Partial Differential Equations - Numerical Methods and Diffpack Programming,. Lecture Notes in Computational Science and Engineering, vol 33. Springer, 2003. 658 p.

    Google Scholar 

  9. G. T. Lines, M. L. Buist, P. Grøttum, A. J. Pullan, J. Sundnes, and A. Tveito. Mathematical models and numerical methods for the forward problem in cardiac electrophysiology. Computing and Visualization in Science, 5:215–239, 2003.

    Article  MATH  Google Scholar 

  10. M. C. MacLachlan, J. Sundnes, and G. Lines. Simulation of st segment changes during subendocardial ischemia using a realistic 3d cardiac geometry. IEEE Transactions on Biomedical Engineering, 52:799–807, 2005.

    Article  Google Scholar 

  11. M. C. MacLachlan, B. F. Nielsen, M. Lysaker, and A. Tveito. Computing the size and location of myocardial ischemia using measurements of ST-segment shift. IEEE Transactions on Biomedical Engineering, 53:1024–1031, 2006.

    Article  Google Scholar 

  12. J. Sundnes, G. T. Lines, and A. Tveito. Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells. Mathematical Biosciences, 172:55–72, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. Sundnes, G. T. Lines, K. A. Mardal, and A. Tveito. Multigrid block preconditioning for a coupled system of partial differential equations modeling the electrical activity in the heart. Computer Methods in Biomechanics and Biomedical Engineering, 5:397–409, 2002.

    Article  Google Scholar 

  14. M. Hanslien, J. Sundnes, and A. Tveito. An unconditionally stable numerical method for the luo-rudy 1 model used in simulations of defibrillation. Mathematical Biosciences, 208:375–392, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Sundnes, G. T. Lines, and A. Tveito. An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso. Mathematical Biosciences, 194:233–248, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Sundnes, B. F. Nielsen, K. A. Mardal, X. Cai, G. T. Lines, and A. Tveito. On the computational complexity of the bidomain and the monodomain models of electrophysiology. Annals of Biomedical Engineering, 34:1088–1097, 2006.

    Article  Google Scholar 

  17. S. O. Linge, G. T. Lines, J. Sundnes, and A. Tveito. On the frequency of automaticity during ischemia in simulations based on stochastic perturbations of the luo-rudy 1 model. Computers in biology and medicine, 38:1218–1227, 2008.

    Article  Google Scholar 

  18. A. Tveito and G. T. Lines. A condition for setting off ectopic waves in computational models of excitable cells. Mathematical Biosciences, 213(2):141–150, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  19. A. Tveito and G. T. Lines. A note on a method for determining advantageous properties of an anti-arrhythmic drug based on a mathematical model of cardiac cells. Mathematical Biosciences, 217(2):167–173, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  20. C. Johnson, D. Keyes, and U. Ruede. Special issue on computational science and engineering. SIAM Journal on Scientific Computing, 30(6):vii–vii, 2008.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Langtangen, H.P., Sundnes, J. (2010). Scientific Computing - Why, What, How and What's Next. In: Tveito, A., Bruaset, A., Lysne, O. (eds) Simula Research Laboratory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01156-6_18

Download citation

Publish with us

Policies and ethics