The goal of COMSOL Access is to provide a forum for you to communicate effectively with COMSOL as well as your colleagues within the multiphysics simulation community. This involves providing you with access to technical support and downloads of the latest {:comsol} software releases, as well as the ability to share your comments and work with other users of the {:comsol} software through forums such as the blog, discussion forum, and Application Exchange. In order to make this an efficient and pleasant experience for you and other members of COMSOL Access, we ask that you follow a few rules and guidelines.
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is the (again, local) scalar product of (cx,cy,cz) and (nx,ny,nz). But since (nx,ny,nz) is a unit normal to the surface, this scalar product nicely extracts the projection of the (cx,cy,cz) vector normal to that surface. In contrast, your quantity D, which (if I understand you correctly) is an ordinary scalar (which may or may not be spatially dependent, but is still a scaler). Multiplying a vector by a scalar simply "scales" the vector. And yes, you may have a good reason to do that. But it is not the same thing as forming the "scaler product" between two vectors. Ok, now notice how your final expression strangely attempts to form a new triplet of numbers by separately multiplying the x,y, and z components of two other vectors together? That is not a standard vector operation. I.e., one does not normally have any good physical reason to take two vectors, say: (Ax,Ay,Az) and (Bx,By,Bz) and form the abnormal-triplet construction: (AxBx,AyBy,AzBz). You see, that kind of operation is neither a scalar (aka "dot") product nor a vector (aka "cross") product. Computing that sort of thing is possible (and the software won't stop you from doing it) but it isn't likely to correspond to anything physical.