Abstract

Numerical techniques are essential in solving the equations governing magma dynamics. Discretizing these equations results in very large systems of (non)linear algebraic equations. For many simulations in two spatial dimensions one can easily use direct methods to solve these discrete systems. For simulations in three dimensions, however, iterative methods are vital since direct methods quickly become very inefficient.

Efficiency of the numerical techniques used to solve the equations of coupled magma/mantle dynamics for a large part depends on the efficiency of the iterative method used to solve the system of algebraic equations. Preconditioners play a very important role in the efficiency of iterative methods as I will discuss in more detail in this talk.

This talk is will be divided into three parts. I will first give an introduction to preconditioners and the challenge of iterative methods for magma dynamics. Afterwards I will discuss the development and analysis of preconditioners designed especially for models of coupled magma/mantle dynamics. I will end this talk by discussing future directions of computational magma dynamics.