"I don't actually understand why you would want to do that. If I understand correctly, then you have a function f(x,y) = g(x) + h(x) which you interpolate or project onto a grid without very specific properties to get f^h(x,y) and you observe that f^h is no longer a sum of functions of x and y separately.
What isn't clear to me why that bothers you. If you don't like it, just project g and h to the mesh separately, or even better project them onto 1d meshes. If you have a situation where you are dealing with functions of one argument, treat them as functions of one argument." f(x,y) = g(x)+h(y) is just for this example that I showed you. The function f is in general dependent on x and y, and in most versions of f, they are not separated. The fact that f^h is no longer separated changes the solution of my pde drastically: If I run my program with the analytical f or with f^h on the axis parallel grid, the output is quite similar. This is not so if I run it with f^h defined on the rotated grid. And since the axis parallel grid is able to capture the separation, I hoped the rotated grid can capture it too. But if I understood you correctly, there is no obvious workaround for this issue , right? Best, Math Wolfgang Bangerth <bange...@colostate.edu> schrieb am Fr., 9. Juni 2023, 17:45: > On 6/9/23 09:14, Mathieu wrote: > > > > I would have to refine the rotated grid roughly seven times to > approximate > > this decoupling accurately. > > Unfortunately, I can refine the grid globally at most twice. > > Do you have an idea how to capture the above decoupling also at the > rotated > > grid better -- > > maybe by generating the grid differently? > > The input to my grid are four points which represent the minimal > bounding box > > of a set of points in 2d > > and the grid should roughly represent this box. > > I don't actually understand why you would want to do that. If I understand > correctly, then you have a function > f(x,y) = g(x) + h(x) > which you interpolate or project onto a grid without very specific > properties > to get > f^h(x,y) > and you observe that f^h is no longer a sum of functions of x and y > separately. > > What isn't clear to me why that bothers you. If you don't like it, just > project g and h to the mesh separately, or even better project them onto > 1d > meshes. If you have a situation where you are dealing with functions of > one > argument, treat them as functions of one argument. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bange...@colostate.edu > www: http://www.math.colostate.edu/~bangerth/ > > > -- > 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 a topic in the > Google Groups "deal.II User Group" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/dealii/QopdaFOjy04/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > dealii+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/dealii/a29f5219-fea7-9cbf-efd8-07aa48ffed49%40colostate.edu > . > > -- 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. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CA%2BwBsdNQj5vDAa74aVfL%3DYXZVpfK5W%2BEuhVcbw5gXv9QzchJ5A%40mail.gmail.com.
