MOLE Library Publications

MOLE Library Publications#

The documents and publications in this page highlight some of the early successes of the MOLE Library, as well as accomplishments from using mimetic differences in the solution of Partial Differential Equations.

Introduction to Mimetic Methods and MOLE#

  • J.E. Castillo and R.D. Grone, A matrix analysis approach to higher-order approximations for divergence and gradients satisfying a global conservation law, SIAM J. Matrix Anal. Appl., Vol. 25, No. 1, pp. 128-142, 2003. doi.org/10.1137/S089547980139802.

  • M. Dumett and J.E. Castillo, General Framework for Mimetic Differences Publication Number: CSRCR2024-07, June 2024.

  • J. Corbino, M. Dumett and J.E. Castillo, MOLE: Mimetic Operators Library Enhanced, The Journal of Open Source Software, 9(99), 6288 (2024), https://doi.org/10.21105/joss.06288.

  • J. Corbino, and J.E. Castillo, High-order mimetic finite-difference operators satisfying the extended Gauss divergence theorem, J. Comput. Appl. Math., v. 364, 2020, 112326.https://doi.org/10.1016/j.cam.2019.06.042.

  • J. E. Castillo and M. Yasuda, Linear Systems Arising for Second-Order Mimetic Divergence and Gradient Discretizations, Journal of Mathematical Modelling and Algorithms, 4(1), 67–82. https://doi.org/10.1007/s10852-004-3523-1.

Advantages of Mimetic Methods Over Other Methods#

Scientific Applications Using MOLE#

  • M. Ferrer, J. De La Puente, A. Farrés, and J. E. Castillo, 3D Viscoelastic Anisotropic Seismic Modeling with High-Order Mimetic Finite Differences, ICOSAHOM 2014, Lecture Notes in Computational Science and Engineering 106, DOI 10.1007/978-3-319-19800-2_18.