An elliptic, quasi-orthogonal grid generation system is formulated based on
quasi-conformal mapping for arbitrary anisotropic (long and skinny) region
s. The resulting system is a generalization of the well-known elliptic grid
generation system derived from conformal mapping. Coupled with the grid ge
neration system, the impedance-matching principle describes a methodology f
or preserving the discrete accuracy of the simulation, both internal to the
domain and near internal geometric interfaces. Empirically, satisfying the
impedance principle tends to minimize mesh effects on the solution results
; meshes that are impedance-matched tend to reduce or eliminate spurious wa
ve reflection and/or attenuation at internal interfaces. The resulting grid
generation system is used to construct impedance-matched quasi-orthogonal
grids on domains containing internal geometric constraints given an algebra
ic grid and a grid impedance function as initial conditions.