On Adaptive Mesh Generation in Two Dimensions
D'Azevedo, E. F.
Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.109-117, October 1999
E. F. D'Azevedo
Computer Science and Mathematics Division,
Oak Ridge National Laboratory
This work considers the effectiveness of using anisomptic coordinate
transformation in adaptive mesh generation. The anisotropic coordinate
transformation is derived by interpreting the Hessian matrix of the data
function as a metric tensor that measures the local approximation error. THe
Hessian matrix contains information about the local curvature of the surface and
gives guidance in the aspect ration and orientation for mesh generation. SInce
theoretically an asymptotically optimally efficient mesh can be produced by
transforming a regular mesh of optimal shape elements, it would be interesting
to compare this approach with existing techniques in solution adaptive meshes.
PLTMG, a general elliptic solver, is used to generate solution adapted
triangular meshes for comparison. The solver has the capability of performing a
posterior error estimate in performing longest edge refinement, vertex
unrefinement, and mesh smoothing. Numerical experiments on three simple problems
suggest the methodology employed in PLTMG is effective in generation near
optimally efficient meshes.
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