On Wed, Jun 15, 2011 at 11:50 AM, Igor <gozdawa.a...@googlemail.com> wrote: > > Hello all, > > does anybody have an idea how to perform integration of fipy > CellVariables over one of the "variables" representing cell centers of > 2D mesh? > > For example: > > dx=0.1 > dy=0.2 > nx=10 > ny=10 > mesh_xy=Grid2D(dx = dx, dy = dy, nx = nx, ny = ny) > xc,yc=mesh_xy.getCellCenters() > > def F(x,y): > return x+y > > N=CellVariable(mesh=mesh_xy, value=F(xc,yc))
A low order approximation is simply (N * mesh.getCellVolumes()).sum() when N is defined to be point locations. > F(x,y) is for illustrative purposes only. In general N will be a > solution of conv-diff. problem at given time. In that case (N * mesh.getCellVolumes()).sum() is no longer an approximation since N is defined as the cell average in the FVM (not the value of N at a given location). Obviously, the derivation of N using the numerical approximation will have an associated error, but the integral is error free. > I'd like to know int_A^B N*yc*dy, A and B are some limits. Just need to create a mask defining some region. mask = (x > 0.5) & (y > 0.2) integral = (mask * N * mesh.getCellVolumes()).sum() for example. > I would > also like the result be of ndarray type (i.e., representing the > integrated value at each xc). Not sure what you are asking. The integral is obviously independent of location. Hope the above helps. -- Daniel Wheeler
