Complex Boundary Integral Equation Formulation and Stability Analysis of a Maxwell Model and of an Elastic Model of Solid-Solid Phase Transformations
- Author(s): Greengard, Daniel Bijan
- Advisor(s): Wilkening, Jon
- et al.
We study a viscoelastic model of the solid-solid phase change of
olivine to its denser $\beta$-spinel state at high pressures and
temperatures reachable in laboratory experiments matching conditions
typical of Earth's mantle. Using a previously unknown technique, the
equations are transformed to the problem of finding two complex
analytic functions in the sample satisfying certain conditions on the
outer boundary. The Sherman-Lauricella boundary integral equation is
used in a numerical algorithm that eliminates the bottleneck of having
to solve a large matrix equation at every timestep. The method is
implemented and used to compute the solution of a number of
non-axisymmetric test problems, some static and some dynamic in time.
Next we develop an alternative formulation in which the Lam