Jacobian-Weighted Elliptic Grid Generation

Authors:
Patrick M. Knupp
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1996

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Abstract

Variational grid generation techniques are used to derive and analyze a weighted elliptic grid generator that controls the Jacobian of the underlying transformation in a least-squares sense. The Euler--Lagrange equations for the area and volume generators are weighted forms of the well-known Laplace generator. Weights are restricted to the class of P-matrices to help achieve global invertibility of the map. Connecting the weights to the Jacobian of the map results in an intuitive means of controlling grid spacing, area, orthogonality, and grid-line directions. Examples are given on the unit square to demonstrate point attraction, local refinement, directional alignment, and adaption to a shock.