Unable to get accurate solution of Laplace Equation in the presence of curved Dirichlet boundary.

[raghwendra-78]

Hi,

I am trying to calculate electric field enhancement factor at the apex of a hemi-ellipsoidal protrusion on a cathode plate in a parallel-plate diode where two conducting plate are kept at a distance 'd'. Cathode is assumed to be at zero potential and anode is at some fixed potential 'V'. Side walls are homogeneous 'Neumann' boundary.

For this purpose I am using libmesh-1.6.1 (compiled with petsc-3.15.1). Geometry and Mesh of the diode was created using Salome Platform and mesh file was exported in unv format . I adapted introduction_ex4.C file given example/introduction

Program file: introduction_ex4 -C.txt

Mesh file for just two plates: cube-unv.txt

Mesh file for diode with hemi ellipsoid: At present I am unable to upload the file, may be due to large size of the file. Later I will post a link to the file in the thread.

In case of simple diode with two plates; cathode at zero and anode at 1000 volt, d=200 mm ( two Dirichlet boundaries and four homogeneous Neumann boundaries (side walls of the diode)), I get desired result, electric field is 5 V/mm.

When I solve the problem with hemi-ellipsoidal protrusion of height 40 mm on the cathode plate, it is expected that electric field at a point situated far-away from the protrusion should be same as that in the absence of protrusion. However I get 5.158 V/mm instead of 5.0 V/mm. I compared the field enhancement factor at the apex of the protrusion calculated using libMesh and AC/DC module of Comsol Multiphysics software as well. libMesh example program underpredicts the enhancement factor.

I shall highly appreciate any suggestion to improve the simulation result. (output log file and slice of solution of protrusion problem with mesh are attached below)

simulation-hemi-ellipsoid

log.txt

Thanks.

Raghwendra Kumar

[raghwendra-78]

Perhaps I should have posted in discussions section. Posted there.