Prolongation

Useful references

• Mongwane - Toward a Consistent Framework for High Order Mesh Refinement Schemes in Numerical Relativity, https://arxiv.org/abs/1504.07609, Sec. 2.4.1
• Carpenter et al. - The Theoretical Accuracy of Runge--Kutta Time Discretizations for the Initial Boundary Value Problem: A Study of the Boundary Error, http://epubs.siam.org/doi/abs/10.1137/0916072
• Shen - Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations, http://www.sciencedirect.com/science/article/pii/S0021999111000908?via%3Dihub

Meeting - 07-Aug-2017

Ian: RK4 expressions we will use to prolongate.

Tasks for next meeting:

Eloisa:

• Set up test cases for space-independent Einstein solutions:
  • Convergence of unigrid - 4th order
  • Convergence of FMR, 2 level, with standard buffer zones. Expect 2nd order error at fixed t (due to order of time interpolation; three points, O(dt^3) local error, O(dt^2) error when integrated up to fixed t)
  • Convergence of FMR, 2 level, without buffer zones, and prolongating on every MoL substep. Expect 1nd order (Carpenter paper).
• Derive k4 if possible

Ian:

• Check we understand all the formulas and the algorithm
• Write out a complete description of what we want to implement

Roland:

• Look at MoL and Carpet and work out what sorts of functions need to be inserted/scheduled/adapted to implement the scheme

Sibo:

• For 1D python code, measure convergence in time for spatially-constant initial data with buffer zones - should be 2nd order at fixed t (I think)

Tomorrow we resync, to make sure we all understand all the parts.

Meeting - 08-Aug-2017

Tasks for next meeting:

Eloisa:

• Add resolution to the FMR test runs in 1D
• Finish derivation of the ks

Ian:

• Hash out a few Cactus function outlines for computing things, prolongating, etc, and schedules. Discuss tomorrow.

Roland:

• Look at the Cactus functions as well
• Think about the regridding issue
• Look at the python code again