Adaptive discrete harmonic grid generation

An heuristic finite difference scheme on irregular plane regions

“…The domains of interest here are simply connected polygonal domains -mostly irregular-which can not be decomposed into rectangles. For such domains, it is possible to generate suitable convex structured grids using the direct optimization method, as discussed in detail in [3,10,12,13,16]. To introduce the required notation for the grids, let m and n be the number of "vertical" and "horizontal" numbers of nodes on the "sides" of a typical domain boundary; the latter is the positively oriented polygonal Jordan curve γ of vertices…”

Numerical Solution of Differential Equations in Irregular Plane Regions Using Quality Structured Convex Grids

“…Further properties of this functional, as well as the algorithm for updating its parameter has been reported in Ref. [2] and Ref. [5].…”

“…The latter consists of minimizing an appropriate functional [6,9,10,13]. Area and harmonic functionals can be used for gridding a wide variety of simple connected domains in the plane [2,3,4,11,16,17], whose boundaries are closed polygonal Jordan curves with positive orientation. If m and n represent the "vertical" and "horizontal" numbers of points of the "sides", then the boundary is the positively oriented polygonal curve γ of vertices V = {v 1 , • • • , v 2(m+n−2) }, and it defines the typical domain Ω.…”

“…[5], and the length functional L(G) with weight σ = 0.5 (See Ref. [2]). The parameter ω, which is a scale factor, can be updated in such a way that in a finite number of updates the combined functional attain its minima within the set of convex grids for Ω if the latter is nonempty.…”