Talk:Mesh generation

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I was tempted to add more but I am only a student of the field and am by no means knowledgeable enough for a comprehensive treatment of the subject. Anyone? Averisk 03:30, 1 November 2005 (UTC)

[edit] mesh generation

I believe that the definition given in Wikipedia on mesh generation is too restrictive. A polygonal decomposition of space will only appy to 2-dimensional domains. I propose following the definition given 'Handbook of Grid Generation' by J. F. Thompson, B. K. Soni, and N. P. Weatherhil:

Mesh Generation is the field dedicated to the study of algorithms used to create a set of points P in Rⁿ with an associated topological interconnectivity distributed over a calculation field for a numerical solution of a set of partial differential equations. The topology is dictated by the type of numerical scheme used to solve a particular partial differential equation, and may be structured, or unstructured.

A mesh is structured if the associated topology on the set of points P is defined by a bijective map

f : Π{0, ..., m_i} -> P,

where Π{0, ..., m_i} is the product of the collection of sets of integers {0, ..., m_i}, for i = 0 to N.

This definition is extended to include a collection of structured sets; in this case, the set of points is said to be a multi-block structured mesh.

A mesh is unstructured otherwise. Every structured mesh can be converted to an unstructured mesh, but the reverse is not necessarily true. An unstructured mesh is a discretization of a bounded set in Rⁿ. The components of the discretization are called elements. The most common elements used in Finite Element Analysis are hexahedra, tetrahedra, triangles, and quadrilaterals.