[Getdp] Setting up a 2nd order electrostatics calculation

John_V jvillar.john at gmail.com
Wed May 12 15:56:11 CEST 2010


I hope you will forgive (or be relieved by!) what is doubtless a simple
question. I am new, not only to Getdp, but also to finite element methods
generally. I am trying to build my way up to solution of my electrostatics
problems by starting with the provided examples and gradually increasing the
complexity, learning one thing at a time.

I have successfully solved a 2-D electrostatics problem with source terms
(free charge) using first order elements. When I attempt to solve the same
problem with 2nd order elements, I get this error:

GetDP   : P r o c e s s i n g . . .
GetDP   : Generate[Sys_Ele]
GetDP   : Unkown type of Element in BF_GradNode_2E
Info    : ...done running 'GetDP'

To go from 1st order to 2nd order I made these changes:

To the .geo file -- no change

To the .msh file produced by Gmsh -- After production of 2-D mesh I click
2nd order before saving.

To the problem definition .pro file -- no change. In case it's relevant
(e.g., for boundary conditions), my geometry consists of concentric circles.
The outer circle is at a fixed potential, defined by a Dirichlet constraint.
The inner circle bounds a region ("Charged") of constant charge density,
rho[Charged] = constant; rho[Air] = 0.;

To the EleSta_v formulation .pro file -- I added the lines { Name s2;
NameOfCoef v2; Function BF_Node_2E; Support DomainCC_Ele; Entity NodesOf[
All ]; } to the FunctionSpace BasisFunction and    { NameOfCoef v2;
EntityType NodesOf; NameOfConstraint ElectricScalarPotential; } to the
FunctionSpace Constraint.

To the Integration_lib.pro file I added a case: { GeoElement Triangle2;
NumberOfPoints  6 ; } to the GradGrad integration.

To the Jacobian_lib.pro file -- no change.

Evidently I have left something out or done something wrong. What?

Thanks in advance for your suggestions.

John

P.S. Background: I'm working on interaction of electron beams with samples
that have insulating regions. I have a simulator that takes care of
scattering calculations including electron cascade. My interest in the above
problem is to determine electric fields due to the charge distribution
predicted by my simulator. The samples may be complex in geometry, with
insulating and conducting regions. Some of the latter may be held at fixed
potentials, others floating. I will have a large number of such problems to
solve, differing from one another mainly in the charge distribution.

I am trying to become more familiar with FEA by reading some elementary
texts. However, none of the ones I have read so far are giving me
sufficiently good insight into the underpinnings of Getdp. Possibly they are
too elementary. Can you recommend some good reading -- something preferably
that develops the subject in terms of objects (function spaces, etc.) that
one encounters in Getdp?
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