Implicit methods

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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)