7 Future plans for ASPECT

We have a number of near-term plans for ASPECT that we hope to implement soon:

• Better ways to deal with the nonlinearity: The simplest algorithm to deal with the nonlinearity of the equations is to use the velocity, pressure and temperature of the previous time step to evaluate the coefficients that appear in the flow equations (1)–(2); and the velocity and pressure of the current time step as well as the previous time step’s temperature to evaluate the coefficients in the temperature equation (3). A slight improvement of this scheme – and the one that is the default in ASPECT – is to use velocities, pressures, and temperatures that are extrapolated from previous time steps to the current time. This is an appropriate strategy if the model is not too nonlinear; however, it introduces inaccuracies and limits the size of the time step if coefficients strongly depend on the solution variables.

  To avoid this, one can iterate out the equations using either a fixed point or Newton scheme. Both approaches ensure that at the end of a time step, the values of coefficients and solution variables are consistent. On the other hand, one may have to solve the linear systems that describe a time step more than once, increasing the computational effort.

  ASPECT currently already implements methods that iterate out the nonlinearity based on various fixed point strategies. These are based on some earlier experiments by Jennifer Worthen [Wor12]. What is missing, though, is a proper Newton method.

• Faster 3d computations: Whichever way you look at it, 3d computations are expensive. In parallel computations, the Stokes solve currently takes upward of 90% of the overall wallclock time, suggesting an obvious target for improvements based on better algorithms as well as from profiling the code to find hot spots. In particular, playing with better solver and/or preconditioner options would seem to be a useful goal.
• More, and more realistic material models: The number of material models available in ASPECT is sizeable, but it does not include all models that have in the past been used in the literature. On the other hand, how realistic a simulation is depends on how realistic the used material model is. We hope to obtain more descriptions of realistic material descriptions over time, either given analytically or based on table-lookup of material properties.