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# Dirichlet boundary conditions

In this section we describe, how functions are computed which take given Dirichlet values. For reasons of simplicity we stick to the two-dimensional case. The extension to higher dimensions is straightforward.

Assume there is a function of boundary values on the face . A particular simple function which interpolates on is given by means of the wavelet coefficients of . Let be the set of 2-dimensional indices and the set of (d-1)-dimensional subindices representing the (d-1)-dimensional adaptive grid on . Then,

In the example, is shown below on the left side and the resulting function is depicted on the right side. The adaptive grid, was a level 5 regular sparse grid.

The function was computed using the member function AdaptiveData<D>::SetBoundaryValueFunction. Up to now, this function is implemented for AdaptiveData<D> only.

In the same fashion as above we can deal with Dirichlet BC on all four faces. In this case we do not only set the coefficients but also the coefficients . A resulting function may look like

For more information on how to generate functions with given Dirichlet values, especially the case then the Dirichlet-values on the different faces do not collapse on corners or edges, we refer to the programming reference of AdaptiveData<D>::SetBoundaryValueFunction.

Next: Neumann boundary conditions Up: Boundary Conditions Previous: Homogeneous or periodic boundary
koster 2003-07-29