Grid Generation and Adaptation byMonge-Kantorovich Optimization in Two andThree Dimensions
Finn, John M., Gian Luca Delzanno, and Luis Chacon
Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.551-568, October 12-15 2008
17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008
T-15, Plasma Theory, Los Alamos National Laboratory, Mail stop: K717,
Los Alamos, NM 87545
The derivation of the Monge-Ampere (MA) equation, as it results from a
variational principle involving grid displacement, is outlined in two dimensions (2D).
This equation, a major element of Monge-Kantorovich (MK) optimization, is discussed
both in the context of grid generation and grid adaptation. It is shown that grids which
are generated by theMA equation also satisfy equations of an alternate variational principle
minimizing grid distortion. Numerical results are shown, indicating robustness to
grid tangling. Comparison is made with the deformation method [G. Liao and D. Anderson,
Appl. Analysis 44, 285 (1992)], the existing method of equidistribution. A formulation
is given for more general physical domains, including those with curved boundary
segments. The Monge-Ampere equation is also derived in three dimensions (3D). Several
numerical examples, both with more general 2D domains and in 3D, are given.
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