Dear Maxi,
I am not an expert in deal.ii. I have a project which is very similar to
your project. I was wondering if it is possible to contact you.
Best,
On Sat, 18 Jan 2020, 14:41 'Maxi Miller' via deal.II User Group, <
dealii@googlegroups.com> wrote:
> I tried to implement a solver for the non-linear diffusion equation
> (\partial_t u = grad(u(grad u)) - f) using the TimeStepping-Class, the
> EmbeddedExplicitRungeKutta-Method and (for assembly) the matrix-free
> approach. For initial tests I used the linear heat equation with the
> solution u = exp(-pi * pi * t) * sin(pi * x) * sin(pi * y) and the assembly
> routine
> template <int dim, int degree, int n_points_1d>
> void LaplaceOperator<dim, degree, n_points_1d>::local_apply_cell(
> const MatrixFree<dim, Number> & data,
> vector_t & dst,
> const vector_t &src,
> const std::pair<unsigned int, unsigned int> & cell_range)
> const
> {
> FEEvaluation<dim, degree, n_points_1d, n_components_to_use, Number
> > phi(data);
>
> for (unsigned int cell = cell_range.first; cell < cell_range.
> second; ++cell)
> {
> phi.reinit(cell);
> phi.read_dof_values_plain(src);
> phi.evaluate(false, true);
> for (unsigned int q = 0; q < phi.n_q_points; ++q)
> {
> auto gradient_coefficient = calculate_gradient_coefficient
> (phi.get_gradient(q));
> phi.submit_gradient(gradient_coefficient, q);
> }
> phi.integrate_scatter(false, true, dst);
> }
> }
>
>
> and
> template <int dim, typename Number>
> inline DEAL_II_ALWAYS_INLINE
> Tensor<1, n_components_to_use, Tensor<1, dim, Number>>
> calculate_gradient_coefficient(
> #if defined(USE_NONLINEAR) || defined(USE_ADVECTION)
> const Tensor<1, n_components_to_use, Number> &input_value,
> #endif
> const Tensor<1, n_components_to_use, Tensor<1, dim, Number>> &
> input_gradient){
> Tensor<1, n_components_to_use, Tensor<1, dim, Number>> ret_val;
> for(size_t component = 0; component < n_components_to_use; ++
> component){
> for(size_t d = 0; d < dim; ++d){
> ret_val[component][d] = -1. / (2 * M_PI * M_PI) *
> input_gradient[component][d];
> }
> }
> return ret_val;
> }
>
>
> This approach works, and delivers correct results. Now I wanted to test
> the same approach for the non-linear diffusion equation with f = -exp(-2 *
> pi^2 * t) * 0.5 * pi^2 * (-cos(2 * pi * (x - y)) - cos(2 * pi * (x + y)) +
> cos(2 * pi * x) + cos(2 * pi * y)), which should be the solution to grad(u
> (grad u)) with u = exp(-pi^2*t) * sin(pi * x) * sin(pi * y). Thus, I
> changed the routines to
> template <int dim, int degree, int n_points_1d>
> void LaplaceOperator<dim, degree, n_points_1d>::local_apply_cell(
> const MatrixFree<dim, Number> & data,
> vector_t & dst,
> const vector_t &src,
> const std::pair<unsigned int, unsigned int> & cell_range)
> const
> {
> FEEvaluation<dim, degree, n_points_1d, n_components_to_use, Number
> > phi(data);
>
> for (unsigned int cell = cell_range.first; cell < cell_range.
> second; ++cell)
> {
> phi.reinit(cell);
> phi.read_dof_values_plain(src);
> phi.evaluate(true, true);
> for(size_t q = 0; q < phi.n_q_points; ++q){
> auto value = phi.get_value(q);
> auto gradient = phi.get_gradient(q);
> phi.submit_value(calculate_value_coefficient(value,
> phi.
> quadrature_point(q),
> local_time),
> q);
> phi.submit_gradient(calculate_gradient_coefficient(value,
> gradient
> ), q);
> }
> phi.integrate_scatter(true, true, dst);
> }
> }
>
> and
> template <int dim, typename Number>
> inline DEAL_II_ALWAYS_INLINE
> Tensor<1, n_components_to_use, Number> calculate_value_coefficient(
> const Tensor<1, n_components_to_use, Number> &input_value,
>
> const Point<dim, Number> &point,
>
> const double &time){
> Tensor<1, n_components_to_use, Number> ret_val;
> //(void) input_value;
> (void) input_value;
> for(size_t component = 0; component < n_components_to_use; ++
> component){
> const double x = point[component][0];
> const double y = point[component][1];
> ret_val[component] = (- exp(-2 * M_PI * M_PI * time)
> * 0.5 * M_PI * M_PI * (-cos(2 * M_PI * (x
> - y))
> - cos(2 * M_PI *
> (x + y))
> + cos(2 * M_PI *
> x)
> + cos(2 * M_PI *
> y)))
> ;
> }
> return ret_val;
> }
>
> template <int dim, typename Number>
> inline DEAL_II_ALWAYS_INLINE
> Tensor<1, n_components_to_use, Tensor<1, dim, Number>>
> calculate_gradient_coefficient(
> #if defined(USE_NONLINEAR) || defined(USE_ADVECTION)
> const Tensor<1, n_components_to_use, Number> &input_value,
> #endif
> const Tensor<1, n_components_to_use, Tensor<1, dim, Number>> &
> input_gradient){
> Tensor<1, n_components_to_use, Tensor<1, dim, Number>> ret_val;
> for(size_t component = 0; component < n_components_to_use; ++
> component){
> for(size_t d = 0; d < dim; ++d){
> ret_val[component][d] = -1. * input_value[component] *
> input_gradient[component][d];
> }
> }
> return ret_val;
> }
>
> Unfortunately, now the result is not correct anymore. The initial
> sin-shape is spreading out in both x- and y-direction, leading to wrong
> results.Therefore I was wondering if I just implemented the functions in a
> wrong way, or if there could be something else wrong?
> Thanks!
>
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