Model Reduction for forward solutions

EIT estimates the internal conductivity distribution from body surface electrodes via the solution of an
inverse problem. Most approaches require solution of a forward problem based on a finite element model (FEM) of
the medium of interest. For iterative solvers, the solution time is typically dominated by the time to solve the FEM
(both for estimation of the measurements and the Jacobian) at each iteration. There is thus a strong incentive to
develop techniques to reduce the solution time.
To obtain accurate forward solutions, it is typically necessary to model a large region far away from the electrodes.
This is most severe in geophysical or endoscopic EIT applications where the medium is effectively infinite. However,
it is also true of traditional EIT applications where, for example, the chest extends above and below the electrode
plane(s). In these extended regions, we do not actually need so solve for the internal voltages; we simply need to
model the effect of the extended region on the ROI. This effect can be thought of in two ways: 1) the extended
region’s effect can be represented by its Dirichlet to Neumann map, or 2) in a resistor model representation of the
FEM, the extended region can be replaced by an equivalent N-port resistor mesh (with 0.5 × N × (N + 1) resistors)
Objective: To implement the model reduction scheme and verify its accuracy and improved calculation time.