DASPK: A new high order and adaptive time-integration technique with applications to mantle convection with strongly temperature-and pressure-dependent rheology

Abstract A new technique is presented for the efficient time-integration of the equations that describe the slow deformation in the Earth's mantle. This method is based on the adaptive, high order implicit solver for differential-algebraic equations (DASPK) and is independent of the choice 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 performed at much lower computational cost, but at the same or higher accuracy, compared to a traditional implicit second-order method. The solution to the full set of 2-D mantle convection equations is 3 to 4 times 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 with strongly temperature and pres...

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