Visualization of higher order finite elements.

Thompson, David C. ; Pebay, Philippe Pierre ; Crawford, Richard H. ; Khardekar, Rahul Vinay

Sandia National Laboratories

关键词: Differential Equations;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Visualization.;    Polynomials;    Mesh Generation Finite Element Method.;   

DOI  :  10.2172/919127
RP-ID  :  SAND2004-1617
RP-ID  :  AC04-94AL85000
RP-ID  :  919127

美国|英语

来源: UNT Digital Library

【 摘 要 】

Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element: