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)[reply]

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.

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My opinion is that the above definition is fine for a handbook on grid generation, a reference book for people interested in solving PDEs, but is not a good definition for a wikipedia page. I don't think that the above definition would be helpful to the typical wikipedia reader wanting to discover what mesh generation is all about. It is overly mathematical and abstract. It jumps right in to distinguish structured vs. unstructured meshes via bijective maps; again, this is unnecessarily abstract, and this is just one of many distinctions between the types of meshes possible. In my experience it is always a challenge to find the right balance between drawing the boundaries to be inclusive and drawing them so broadly that nothing is distinguished, and accuracy vs. comprehensible. In the sense of polyhedra polygon vs. other meshes the above proposed definition is more broad. It is less broad in restricting its attention to numerical solutions of PDEs. -- Samitch87111 — Preceding unsigned comment added by Samitch87111 (talk • contribs) 16:29, 16 October 2024 (UTC)[reply]

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