Talk:Mesh generation
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 | The contents of the Principles of grid generation page were merged into Mesh generation on 23 October 2022. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
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)
mesh generation[edit]
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, ..., mi} -> P,
where Π{0, ..., mi} is the product of the collection of sets of integers {0, ..., mi}, 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.
External links modified (January 2018)[edit]
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Proposed merge of Principles of grid generation into Mesh generation[edit]
Grid generation already redirects to mesh generation. fgnievinski (talk) 05:19, 23 May 2021 (UTC)
