# Numerical Analysis and Scientific Computing Seminar

## Fast Solvers for Geodynamic Flows

**Speaker:**
Scott MacLachlan, Tufts University

**Location:**
Warren Weaver Hall 1302

**Date:**
Oct. 14, 2011, 10 a.m.

**Synopsis:**

Geodynamic flows, such as the convection within the Earth's mantle, are characterized by the extremely viscous nature of the flow, as well as the dependence of the viscosity on temperature. As such, a PDE-based approach, coupling the (stationary) Stokes Equations for viscous flow with a time-dependent energy equation, offers an accurate mathematical model of these flows. While the theory and practice of solving the Stokes Equations is well-understood in the case of an isoviscous fluid, many open questions remain in the variable-viscosity case that is relevant to mantle convection, where large jumps occur in the fluid viscosity over short spatial scales. I will discuss recent progress on developing efficient parallel solvers for geodynamic flows, using algebraic multigrid methods within block-factorization preconditioners.