In this paper, a procedure is advanced that locates CVBEM nodal point locations on and exterior of the problem boundary such that error in matching problem boundary conditions is reduced.
To obtain a well-posed problem, boundary conditions have to be prescribed on the inflow part of the domain boundary.
A discrete transformation technique together with the boundary point collocation method is employed to evaluate the unknown coefficients of the solution series via satisfying the problem boundary conditions.
The presented procedure results in nodal locations that achieve considerable error reduction over the usual methods of placing nodes on the problem boundary such as at equally spaced locations or other such procedures.
That is, locating the nodal points is part of modeling optimization process, where nodes are not restricted to be located on the problem boundary (as is the typical case) but instead locations are optimized throughout the exterior of the problem domain as part of the modeling procedure.
This method solves the forward problem (boundary radiance at each wavelength) and the inverse problem (spatial distribution of chromophores concentrations) simultaneously using a reduced Hessian sequential quadratic programming (rSQP) method [ 13, 17].
