E. F. D'Azevedo, Optimal triangular mesh generation by coordinate transformation, SIAM J. Sci. Stat. Comput. 12, 755 (1991).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....anisotropic mesh generation [20] This is often done using the Hessian to construct a Riemannian metric tensor that gives the desired edge length as a function of direction. A mesh generation algorithm yielding asymptotically optimally stretched triangles in this manner was given by D Azevedo [6], but his method is restricted to structured meshes and a very small space of surfaces (vertex degree 6 and zero Riemann Christoffel tensor everywhere) Mesh generation methods have been employed to create simplification algorithms by appropriate definition of the desired edge length function. ....

E.F. D'Azevedo, Optimal triangular mesh generation by coordinate transformation, SIAM J. Sci. Statist. Comput. 12 (4) (1991) 755--786.

....center x c , provided that the Hessian matrix of u, denoted by H, is positive de nite. The geometric illustration of interpolation at the vertices of the mesh cell is that the circum surface of the cell from this family of ellipses is the level surface of value zero. It is shown by D Azevedo [6] that for x close to x c , E 0 can be written as 1 Hdx; where dx = x x c and H is calculated at x = x c . Further, D Azevedo and Simpson [7] show that the gradient of the linear interpolation error is given by EG (x) kr(u 1 u)k l 2 Hdx: Writing dx = Jd with d = c , we have ....

E. F. D'Azevedo. Optimal triangular mesh generation by coordinate transformation. SIAM J. Sci. Stat. Comput., 12:755 - 786, 1991.

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E. F. D'Azevedo, Optimal triangular mesh generation by coordinate transformation, SIAM J. Sci. Stat. Comput. 12, 755 (1991).

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