Is any faster version of VectorTools::point_gradient?

[沈键]

Hello,

  I want to compute streamlines in deal.II after solving a velocity potential equation, so I need to get velocity (gradient of solution) on the point to take the streamline a step forward. Unfortunately, each streamline consists around 2000 points which means it should call `VectorTools::point_gradient` 2000 times. It takes too much time. I search the document but find VectorTools::point_gradient only support searching the point belong to which cell globally.  I think it can be optimized, because if I have got previous point, next point should locate in the same cell or neighbor cells. My question is:

  Is any ready-made function of `point_gradient` in deal.II supporting searching the specified point's owner cell only around given cells not globally? 

  Thanks for your reply in advance.

[Daniel Arndt]

Hello,

Have a look at VectorTools::point_gradients (https://www.dealii.org/developer/doxygen/deal.II/namespaceVectorTools.html#aada37fd09d8be1b9ed9bb12d698f8ee4).

Best,

Daniel

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[Wolfgang Bangerth]

>   I want to compute streamlines in deal.II after solving a velocity
> potential equation, so I need to get velocity (gradient of solution) on
> the point to take the streamline a step forward. Unfortunately, each
> streamline consists around 2000 points which means it should call
> `VectorTools::point_gradient` 2000 times. It takes too much time. I
> search the document but find VectorTools::point_gradient only support
> searching the point belong to which cell globally.  I think it can be
> optimized, because if I have got previous point, next point should
> locate in the same cell or neighbor cells. My question is:

To augment the generic solution Daniel already pointed out, let me
mention that Rene Gassmoeller a while ago put a *lot* of work on doing
exactly what you are looking for in ASPECT. This work is documented here:
https://www.math.colostate.edu/~bangerth/publications/2016-particles.pdf
A longer version exists here:
https://arxiv.org/abs/1612.03369

The algorithm described in the paper is implemented starting here, in
ParticleHandler::sort_particles_into_subdomains_and_cells():
https://github.com/dealii/dealii/blob/master/source/particles/particle_handler.cc#L1299

Best
W.

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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/