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# Algorithm for TRACING Boundaries or Interfaces Within Finite Element Meshes

IP.com Disclosure Number: IPCOM000040633D
Original Publication Date: 1987-Dec-01
Included in the Prior Art Database: 2005-Feb-02
Document File: 3 page(s) / 27K

IBM

Lamp, ED: AUTHOR

## Abstract

An algorithm is described for finding and defining regions within a finite element mesh where changes in element properties take place, i.e., a boundary or interface. The algorithm makes a search for elements bordering on a reference element along a side counter- clockwise from a reference node. INPUT: 1) a. To find the boundary of a region, the set of properties included in that region must be specified, e.g., PROP = {P1, P2, P3, ...}. b. To find the interface of two regions, the two disjoint sets of properties included in the regions must be specified, e.g., PROP = {P1, P2, P3, ...} and PROP2 = {P4, P5, ...}, where Pn's are the properties of elements of the regions. 2) An array P giving the properties of the elements Ei, where i = 1...m, such that P(Ei) = Pj, for any valid j.

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Algorithm for TRACING Boundaries or Interfaces Within Finite Element Meshes

An algorithm is described for finding and defining regions within a finite element mesh where changes in element properties take place, i.e., a boundary or interface. The algorithm makes a search for elements bordering on a reference element along a side counter- clockwise from a reference node. INPUT: 1) a. To find the boundary of a region, the set of properties included in that region must be specified, e.g., PROP = {P1, P2, P3,

...}.

b. To find the interface of two regions, the two disjoint sets of

properties included in the regions must be specified, e.g.,

PROP = {P1, P2, P3, ...} and PROP2 = {P4, P5, ...}, where Pn's

are the properties of elements of the regions. 2) An array P giving the properties of the elements Ei, where i = 1...m, such that P(Ei) = Pj, for any valid j. 3) An array N giving the nodes associated with each element Ei, such that N(Ei) = (n', n'', n'''), where the n's are the three

nodes defining corners of a triangle representing each element

Ei . 4) Arrays X and Y giving the X and Y coordinates of the nodes. OUTPUT: An array, BOUNDARY, containing the node numbers of the boundary of a region, ordered along the boundary, or the node numbers of the sections of interface of two regions ordered along the interface with separate interfaces separated by markers. The algorithm follows: INITIAL SET UP: 1) In the array N, for each Ei order the triplets (n's) to be counterclockwise using the arrays X and Y. 2)Find a starting point on the boundary by finding the node with the minimum X-coordinate Xmin and the minimum Y coordinate associated

with Xmin, such that the node is contained in any element of any

property contained in the set PROP. This node is called the

reference node and the element of acceptable pro...