Grade cartesiana

Exemplo de uma grade cartesiana.
Exemplo de uma grade regular.
Exemplo de uma grade retilinear.
Exemplo de uma grade curvilinear.

Uma grade regular é uma tesselação de um Espaço euclidiano de n dimensões criado por paralelepípedos.[1] Grades desse tipo aparecem em papéis milimetrados e podem ser usados em Método dos elementos finitos, assim como em Método dos volumes finitos e em Método das diferenças finitas. Como as derivadas de campo são expressas convenientemente como diferenças finitas,[2] grades estruturadas aparecem muito em métodos de diferença finita. Grades desestruturadas oferecem mais flexibilidade que grades estruturadas e, por isso, são mais úteis em métodos de volume e elementos finitos.

Cada célula na grade pode ser endereçada pelo índice em duas (i,j) ou três (i,j,k) dimensões, e cada vértice tem coordenadas em 2D ou em 3D para algum número real dx, dy e dz representando o espaço da grade.

Grades relacionadas

Uma Grade cartesiana é um caso especial onde os elementos são quadrados unitários ou cubos unitários e os vértices são pontos inteiros.

Uma Grade retilinear é uma tesselação de retângulos ou paralelepípedos que não são, em geral, todos congruentes. As células ainda podem ser indexadas por inteiros, como na grade cartesiana, mas o mapeamento de índices para coordenadas de vértices é menos uniforme que uma grade regular.

Uma Grade curvilinear ou Grade estruturada é uma grade que possui a mesma estrutura de uma grade regular, onde as células são quadriláteras ou cúbicas, ao invés de relangulos e paralelepípedos retangulares.

Ver também

Notas

  • Este artigo foi inicialmente traduzido, total ou parcialmente, do artigo da Wikipédia em inglês cujo título é «Regular Grid».

Referências

  1. ↑ Uznanski, Dan. «Grid.». From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. Consultado em 25 de março de 2012 
  2. ↑ J.F. Thompson, B. K . Soni & N.P. Weatherill (1998). Handbook of Grid Generation. [S.l.]: CRC-Press. ISBN 978-0-8493-2687-5 

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