/compgeodyn

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CERI 7315/8315 Computational Methods for Geodynamics

Instructor: Eunseo Choi

Time and Location: MWF, 10:20 - 11:15 am.

Contact: echoi2@memphis.edu

Grades

  • Topical homeworks: 50 %
  • Term project: 30 %
  • Quizzes: 20 %

Office Hours

  • To be arranged individually
  • Chatting and meeting via MS Teams preferred

Goal and Objectives

This course aims to enable students to understand the basics of the finite element method (FEM), a versatile numerical method for solving partial differential equations.

After taking this course, students will be able to use or modify as necessary the existing community finite element codes (e.g., CIG codes) for their geophysical research.

To achieve the goal, we will

  1. review the fundamental governing equations in continuum mechanics,

  2. have under-the-hood understanding of finite element method,

  3. gain hands-on experience with common procedure and useful practices in computational research,

  4. use one of the open-source FEM codes, possibly after modifications, for their term project.

References and Online Resources

No required textbook but parts of the references listed below will be used.\

Reference texts1

  • Continuum mechanics:

    • $^{\dagger}$ Tadmor, E. B., Elliott, R. S., and Miller, R. E. (2012). Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations. Cambridge University Press, Cambridge
    • Holzapfel, G. A. (2000). Nonlinear solid mechanics : a continuum approach for engineering. Wiley, Chichester ; New York
    • Malvern, L. E. (1977). Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, Upper Saddle River, New Jersey

  • Fundamental numerical techniques

    • $^{\dagger}$ Quarteroni, A., Sacco, R., and Saleri, F. (2000). Numerical Mathematics. Springer-Verlag, New York
    • $^{\dagger}$ Zienkiewicz, O. C., Zhu, J. Z., and Taylor, R. L. (2013). The Finite Element Method: Its Basis and Fundamentals. Butterworth-Heinemann, 7th edition
    • $^{\dagger}$ Ismail-Zadeh, A. and Tackley, P. (2010). Computational Methods for Geodynamics. Cambridge University Press
    • $^{\dagger}$ Gerya, T. (2009). Introduction to Numerical Geodynamic Modelling. Cambridge University Press, New York

  • Geodynamics:

    • Turcotte, D. L. and Schubert, G. (2002). Geodynamics. Cambridge University Press, New York, 2nd edition
    • $^{\dagger}$ Schubert, G., Turcotte, D. L., and Olson, P. (2001). Mantle Convection in the Earth and Planets. Cambridge University Press, Cambridge
    • Davies, G. F. (1999). Dynamic Earth: Plates, Plumes, and Mantle Convection. Cambridge University Press, Cambridge

Online resources

Term projects

  • Students carry out a reasonably small but non-trivial project relevant to the course's goal and objectives.

  • They should use GitHub to manage their projects and products as sharable and reusable resources.

  • A project topic will be decided individually based on students' interests and needs.

  • Possible topics:

    • Consider in a global-scale mantle convection model the effects of centrifugal acceleration in addition to the typical geocentric gravity

    • Reproduce and possibly improve a published work on computational methods.

    • Parallelize an existing code with a directive-based approach such as OpenMP and OpenACC and assess the performance improvement

    • Introduce recent advances in physics-informed neural networks (PINNs)

Course Outline

Footnotes

  1. $^{\dagger}$ means that the UofM Library has an ebook version. ↩