DASPK - A NEW HIGH-ORDER AND ADAPTIVE TIME-INTEGRATION TECHNIQUE WITHAPPLICATIONS TO MANTLE CONVECTION WITH STRONGLY TEMPERATURE-DEPENDENTAND PRESSURE-DEPENDENT RHEOLOGY

A new technique is presented for the efficient time-integration of the equations that describe the slow deformation in the Earth's mantle. T his method is based on the adaptive, high order implicit solver for di fferential-algebraic equations (DASPK) and is independent of the choic e of spatial discretization technique. Using a standard finite element package for the spatial discretization, it is shown that the solution of the 2-D convection-diffusion equation for temperature can be perfo rmed at much lower computational cost, but at the same or higher accur acy, compared to a traditional implicit second-order method. The solut ion to the full set of 2-D mantle convection equations is 3 to 4 limes more efficient. Both in 2-D and 3-D, the memory and CPU-usage of this implementation depends linearly on the number of grid points and has good properties with respect to vectorization and parallelization. As an application of this technique, convection in the Earth's mantle wit h strongly temperature and pressure dependent rheology is studied in a xisymmetric geometry. Models are developed that are consistent with cu rrent estimates of surface heat how and radial viscosity distribution. General characteristics are: a dynamic upper mantle overlying a near- stationary lower mantle; strong plumes rising from the core-mantle bou ndary, even at high rates of internal heating; and an effective Raylei gh number of nearly two orders of magnitudes lower than commonly used values in the rang of 10(7) to 10(8).