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ketch edited this page Nov 7, 2014 · 1 revision

Members

  • Jed Brown
  • Matteo Parsani
  • Lulu Liu

Long term goal

  • Implementation of "some" implicit TS schemes for the solution of stiff geophysical problem

We are maybe aiming too high but one should always do that :-)

Approach

  • Nonlinear geometric multigrid for low-Mach transient problems (finite time step).
  • Multi-stage smoothers (aka explicit Runge-Kutta, similar to polynomial smoothers).
  • Constructing of diagonal preconditioner using wave decomposition.
  • Possible use of matrix-based Gauss-Seidel or ILU smoothers.

Organization:

github repository: https://github.com/mparsani/pyclaw/tree/impl-hpc3

Daily achievements

4 February 2012


  • PETSc can use explicit RK schemes in 3S* low-storage form as smoother for MG. ERK62 has been tested for the lid-driven cavity flow available in PETSc. Its performance are not impressive but it has not been design for damping high-frequencies. In the next weeks we will provide some optimized smoothers. Van Leer smoothers are also available in PETSc now.

  • interpolation of PyClaw aux array available in PETSc. This is required for MG. Piece-wise constant interpolation is done. This is consistent with the well-balancing setup of sharpclaw solver (drop high-order contribution and move down to second-order accurate scheme)