FYS-GEO4510 – Introduction to mechanical geomodeling

Course description

• Course content
• Learning outcome
• Admission
• Prerequisites

• Teaching
• Examination

Course content

Dimensional analysis and scaling. Finite difference methods: diffusion equation in 1d and 2d; elastic wave equation in 1d and 2d; fracture. Approximation techniques: trial functions, and Galerkin’s Finite Element Formulation. Finite Element programming in Matlab: program structure; matrix elements and vectors. Laplace’s and poisson’s equations. Elasticity: plane stress; plane strain; three-dimensional solid: dynamics, thermal stress. Viscous, visco-elastic, and visco-elastoplastic rheologies. Coupling of deformation and fluid flow.

Learning outcome

• The mathematical formulation of geomechanical problems using partial differential equations
• Computer implementation of various numerical techniques with a focus on the finite element method as applied to heat transfer and solid/fluid mechanics
• The theory of linear finite element method for the model parabolic, elliptic, and hyperbolic problems:
  - Approximate solution using the weak form formulation
  - Numerical interpolation, differentiation and integration
  - Isoparametric elements for multidimensional problems
  - Error analysis, stability, convergence
  - Stable discretizations and solution strategies for the incompressible Stokes problem
• Direct and iterative methods for solving linear systems of equations
• Basic solution strategies for coupled non-linear problems

Admission

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Courses with less than three students registrered will normally be cancelled.

Prerequisites

Formal prerequisite knowledge

None

Recommended previous knowledge

Bachelor-degree in physics, geoscience, or applied mathematics.

Teaching

The course is given every spring semester and comprises 30 hours of lectures, 30 hours of computer-based exercises (compulsory submissions), and 30 hours of theoretical exercises, altogether 6 hours per week.

Examination

10 compulsory exercises (Pass/fail). In addition a final oral exam (Pass/fail).

Detailed information about examinations at the Faculty of Mathematics and Natural Sciences can be found here