Numerical Simulation Methods in Geophysics - LV15

This lecture series is a very basic introduction into numerical simulation techniques in geophysics using finite differences. We only consider the equation of continuity, a very simple elliptic partial differential equation that governs, e.g., the DC resistivity method. We will have a look at simple spatial discretization techniques on rectangular grids and solve the corresponding boundary value problem using different boundary conditions. Boiling down the problem to the solution of linear systems of equations we will have a closer look at equation solvers, particularly Krylov subspace methods like the conjugate gradient method. We'll scrutinize different preconditioning methods and finally close with a singularity removal procedure, also called a secondary field approach, which is very popular among electromagnetic geophysicists. The exercises extend the view towards time-dependent parabolic PDEs leading to initial and boundary value problems that govern, e.g., transient electromagnetic fields and other geoelectromagnetic methods.