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  • #139

Closed
Open
Opened Jan 14, 2019 by Lukas Riedel@lriedelOwner0 of 1 task completed0/1 task

Flux reconstruction yields large error on 3D simplices and 2nd order polynomials (only)

The following discussion from !105 (merged) should be addressed:

  • @sospinar started a discussion: (+13 comments)

    I'm having troubles with the \mathcal{RT}_1 elements in 3D. For simplices, the jumps are quite high, while for cubes a local matrix is throwing an error saying that is singular. Not really sure how to proceed here...

Collected info

A single testing case for the flux reconstruction shows strongly increased flux jump residuals:

case error
2D_1_cube < 1E-17
2D_2_cube < 1E-17
2D_3_cube < 1E-17
2D_1_simplex < 1E-17
2D_2_simplex < 1E-17
2D_3_simplex < 1E-17
3D_1_cube < 1E-17
3D_2_cube < 1E-17
3D_3_cube none
3D_1_simplex < 1E-17
3D_2_simplex 2.70125e-11
3D_3_simplex < 1E-17

@sospinar:

We have several sources of numerical inaccuracies

  • In the DG cases, they come because values that should represent the same value are generated by different local matrices; Ax=b problems.
  • In the evaluation of the fluxes, they come from the Piola transformation, which have the following operations:
    auto J = e.geometry().jacobianInverseTransposed(x);   //! Geometry dependent
    J.invert();
    J.umtv(x,y);                                          //! y += A^T x
    y /= J.determinant();

Proposal

@sospinar:

Will forward this question to Prof. Bastian.

How to test the implementation?

Related issues

See #65 (closed), !105 (merged)

Edited Jan 09, 2020 by Lukas Riedel
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Reference: dorie/dorie#139