1887

Abstract

Summary

Optimization algorithms used to solve inverse problems in geoscience have abstract mathematical descriptions – many of them (Conjugate Gradient iteration, Newton’s method,…) are so–called matrix free algorithms, that is, they manipulate their mathematical objects (vectors, functions) without reference to their internal details. Similarly, time-stepping algorithms for dynamical simulation may be described in terms of update rules for dynamical states, without reference to the internal structure of these states or the precise action of the rules. Both of these algorithmic settings provide opportunities for creation of reusable open source code bases, applying to many different tasks. Not only do such libraries save programmer effort and reduce the incidence of errors, but also they could potentially make possible comparison of inversion techniques by providing common implementations for common components. This paper lays out some examples of features that computational types should inherit from their mathematical models, and some solutions to the programming problems that arise in implementing such types.

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/content/papers/10.3997/2214-4609.201601649
2016-05-30
2024-03-28
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References

  1. Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P. and Buschelman, K., Dalcin, L., Eijkhout, V., Gropp, W., Kaushik, D., Knepley, M., Curfman McInnes, L., Rupp, K., Smith, B., Zampini, S. and Zhang, H.
    [2015] PETSc Web page (http://www.mcs.anl.gov/petsc).
    [Google Scholar]
  2. Gockenbach, M., Reynolds, D., Shen, P. and Symes, W.
    [2002] Efficient and automatic implementation of the adjoint state method. ACM Transactions on Mathematical Software, 28, 22–44.
    [Google Scholar]
  3. Heroux, M., Bartlett, R., Howle, V., Hoekstra, R., Hu, J., Kolda, T., Lehoucq, R., Long, K., Pawlowski, R., Phipps, E., Salinger, A., Thornquist, H., Tuminaro, R., Willenbring, J., Williams, A. and Stanley, K.
    [2005] An overview of the Trilinos project. ACM Transactions on Mathematical Software, 31(3), 397–423.
    [Google Scholar]
  4. Holden, J.
    [2015] The genesis of Madagascar. The Leading Edge, 34, 1386–1388.
    [Google Scholar]
  5. Kouri, D., Ridzal, D., van Bloemen Waanders, B. and von Winckel, G.
    [2015] ROL Web page (http://trilinos.org/packages/rol).
    [Google Scholar]
  6. Mathworks
    Mathworks [2015] MATLAB version 8.5.0.197613 (R2015a).The Mathworks, Inc., Natick, Massachusetts.
    [Google Scholar]
  7. Padula, A.D., Symes, W. and Scott, S.D.
    [2009] A software framework for the abstract expression of coordinate-free linear algebra and optimization algorithms. ACM Transactions on Mathematical Software, 36, 8: 1–8: 36.
    [Google Scholar]
  8. Ruelle, D. and Takens, F.
    [1971] On the nature of turbulence. Communications in Mathematical Physics, 20, 167–192.
    [Google Scholar]
  9. Symes, W.W., Sun, D. and Enriquez, M.
    [2011] From modelling to inversion: designing a well-adapted simulator. Geophysical Prospecting, 59, 814–833. DOI:10.1111/j.1365‑2478.2011.00977.x.
    https://doi.org/10.1111/j.1365-2478.2011.00977.x [Google Scholar]
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