On Adaptive Mesh Generation in Two Dimensions

Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.109-117, October 1999

MESHING
RESEARCH
CORNER

Abstract
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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