> > Hi Alex, >> > > Thanks for the clarification, Jean-Paul. >
I'm sorry to say that you shouldn't be too quick in this instance to thank me... > I'm glad to hear that my syntax is correct. > > I am indeed using an extractor, e.g. here's a line from my code: > const Tensor<2, dim> gradv = fe_values[velocity].gradient(j, quad); > Ok, so this demonstrates something that I came to my mind only after I'd posted my reply. What you're asking for on this line is the gradient of the j'th shape function at the quad'th quadrature point. So not the gradient of the velocity (solution) as I'd originally thought. So you'll have to scrap most of what I'd said. I'm not too familiar with FEM implementations of fluids problems, so I'm going to have to defer to other people to help you with the specifics. I wouldn't want to lead you astray... But have you seen the tutorials that deal with Stokes / Navier-Stokes problems, such as step-22 <https://dealii.org/8.4.1/doxygen/deal.II/step_22.html#StokesProblemassemble_system> and 35 <https://dealii.org/8.4.1/doxygen/deal.II/step_35.html#ThecodeNavierStokesProjectionassemble_advection_termcodemethodandrelated>? I know that they don't use this component syntax, but they might give you a better idea as to how to implement your problem in general. You might also find the module on handling vector valued problems <https://dealii.org/8.4.1/doxygen/deal.II/group__vector__valued.html> useful in terms of seeing how the structure of a fluids problem might look like when using / not using extractors in its implementation. > It seems they have to do some work to map to the correct indices, i.e. > with > const unsigned int component_i = fe.system_to_component_index > <https://www.google.com/url?q=https%3A%2F%2Fdealii.org%2Fdeveloper%2Fdoxygen%2Fdeal.II%2FclassFiniteElement.html%23a27220a135402b96c7e6eecbb04acda56&sa=D&sntz=1&usg=AFQjCNH9FPtvXF6muGtnl4nIgc1tGhyt0w> > (i).first; > This is the vector component associated with the i'th shape function. I'm not sure that this is helpful for what you're wanting to implement. This function and its friends are discussed in step-8 and the module on handling vector valued problems <https://dealii.org/8.4.1/doxygen/deal.II/group__vector__valued.html> but, as I said, I don't think it applies here. > When I implement this with higher level library, FEniCS, I don't have to > write the summation; but I think I have to write the summation in deal.II; > hence I need to access $\partial_j z_i$, which I'm doing with the S[i][j] > syntax that we discussed. I actually implement something similar to the > integrand of this operator, for a given quadrature point and degree of > freedom, with the lambda function: > auto c = []( > const Tensor<1, dim> _w, > const Tensor<2, dim> _gradz, > const Tensor<1, dim> _v) > { > double sum = 0.; > > for (unsigned int i = 0; i < dim ; ++i) > { > for (unsigned int j = 0; j < dim; ++j) > { > > > sum += _w[j]*_gradz[i][j]*_v[i]; > > } > } > > return sum; > }; > No, you shouldn't have to do this summation by hand (unless the tensors are incompatible with one another, which is not the case here). The tensor library has a pretty comprehensive set of (well-tested) contraction functions implemented for it. So you'd only need to write const double sum = v*_gradz*w; P.S. What's the best way to communicate math equations on the mailing list? > I'm just typing what I think is roughly the correct LaTeX syntax, but this > seems a bit clunky. > It seems that most of us can get the gist of a LaTex-like notation, but some choose to share PDFs for more elaborate equations or deviations. I don't think that there's a preferred method of communicating this type of information :-/ -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
