Equations
This problem is simply a Poisson problem with Dirichlet boundary conditions on two regions of the boundary and homogeneous Neumann or Robin boundary conditions elsewhere.
On the computation domain , the problem reads:
Unknowns
CEPS ID | Name | Math symbol | Unit |
0 | Electric potential | | |
Tissue properties
- is the conductivity tensor,
- is the Robin coefficient and the boundary condition. It is set to 0 by default (thus changing the BC to homogeneous Neumann). It can be defined as a piecewise constant function of region attributes.
- The domains and are the anode and cathode, respectively. They can be defined using mesh region attributes.
How to use
The specific parameters to set are conductivity
, anode attributes
, cathode attributes
, and robin coefficients
. Default conductivity is 1, default Robin coefficient is 0.
problem type : dirichlet anode cathode
output file name : ./results/poisson
3d mesh : ./meshes/catheterBloodTissue.vtk
conductivity : CONSTANT 1.2 0. 0. 0. 0.4 0. 0. 0. 0.4
anode attributes : 2
cathode attributes : 3
# Optional
# robin coefficients : 1 30
spatial discretization : FE 1
linear solver absolute tolerance : 1.E-12
linear solver relative tolerance : 1.E-12
linear solver type : GMRES