Are the region structure fields (region.x, .y, .z) the centroids of the elements in PDE toolbox (3D Geometry)?

I'm working with a 3D geometry. I use the conductive media DC to calculate the electric potential, then I calculate the joule effect in the centroids and now I want to use it as a heat source (coefficient f) in the heat transfer module. The mesh is always the same.

I've seen that when the f coefficient in the function form is calculated, the region.x,.y,.z is grouped in vectors of 2500 components so I guess matlab repeats the function untill the region fields complets all the mesh size.

The problem appears when I try to assign a f value to the coordinates... it seems that the region.x,.y,.z are not the centroids of the elements...

Does anyone know exactly how the PDE coefficient fucntion form works (Why just 2500 elements in the region.x,.y,.z??)and the real meanning of the region.x,.y,.z field?

Thank you in advance.

Answer 1

[Alan Weiss]

The solvers need to evaluate the coefficients at various locations depending on the type of element, linear or quadratic. Integration over the finite elements is done using Gaussian quadrature, which involves sampling coefficients at Gauss points.

So, no, it is not sufficient to evaluate the coefficients at the centroids of the elements, you must give the coefficients at the requested locations, which are the Gauss points, so that the solver can perform numeric integration as accurately as possible.

Alan Weiss

MATLAB mathematical toolbox documentation

[Oriol Puigde]

Thank you for your answer Mr Weiss, So if the coefficient is evaluated at the Gauss points, the units of "f" in case of a heating source are volumetric? How can we know the input value outside the centroids?

thank you in adavance

[Alan Weiss]

Sorry, I do not understand the details of your application well enough to give you a sensible answer.

Alan Weiss

MATLAB mathematical toolbox documentation