Dear Wolfgang Bangerth,
I'm sorry to reply you in a old question mail, I want to know when rhs
depend on the solution i.e., rhs is a polynomials of the solution, should
we handle it with test function to get a bilinear form while we construct
the weak form?
The description may be confused, for example consider the rhs as
f(u,x,t) in Step-26 (the heat euqation,the original rhs is f(x,t)), f(u,t)
may be u^2+u^3+u^4, how to deal with such a problem?
I have read the toturials to find the answer, but the rhs always only
depend on x,y,z and Step-15 can't answer my question(maybe) .
Best
M.
----------------------------------------------------
email: miffy....@gmail.com
在 2017年8月25日星期五 UTC+8上午9:03:26，Wolfgang Bangerth写道：
>
>
> > where x component of vector_RHS is -(grad_psi)_y / x and y component is
> > (grad_psi) / x (here psi is the another calculated scalar solution)
> >
> > So, I refer to "class AdvectionField : public TensorFunction<1,dim>" in
> > step-9.cc to form the vector_RHS
>
> You're approaching this the wrong way. The Function<dim> and
> TensorFunction<dim> classes are intended to represent functions that only
> depend on x,y or x,y,z. But in your case, your right hand side depends on
> the
> solution itself.
>
> I think you should look into how step-15 builds a right hand side that
> depends
> on the solution. It will probably be something like this:
>
> FEValuesExtractors::Scalar scalar_solution(0);
> std::vector<Tensor<1,dim>> solution_gradients (n_q_points);
> for (cell=...)
> {
> fe_values.reinit(cell);
> fe_values[scalar_solution].get_function_gradients (solution,
>
> solution_gradients);
> for (q=...)
> {
> for (i=...)
> for (j=...)
> cell_matrix(i,j) += ...
>
>
> Tensor<1,dim> rhs;
> Point<dim> q_point = fe_values.quadrature_point(q);
> rhs[0] = solution_gradients[q][1] / q_point[0];
> rhs[1] = solution_gradients[q][0] / q_point[0];
> for (i=...)
> local_rhs(i) = fe_values[scalar_solution].value(i,q) *
> rhs *
> fe_values.JxW (q);
> }
> ...
>
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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