The Finite Element Method In Engineering Problems: Time And Memory Employment Reduction

Some geometrical and evolutionary procedures for optimizing the calculation times of 3D current fields by the finite element method

“…If we refer, for example, to the node i , that is to say to the row i of the matrix C of the coefficients, then:The term C ii contains the sum of as many terms as the tetrahedrons sharing the node i .The term C ij contains the sum of as many terms as the tetrahedrons having the side i ‐ j in common. Obviously, if the node i under examination is not connected with the node j , then C ij =0 (it is well‐known that the matrix of the coefficients C is a very sparse matrix).This row‐by‐row procedure turns out to be long because, for the calculation of each non‐null term of each individual row of C , the program has to read all the N e rows of the “matrix of vertices” V , as thoroughly explained in Settanni et al (1989).…”

“…It is well‐known that in the finite element method the matrix C of the coefficients of the system of linear equations is obtained, in the traditional way, by calculating and by properly assembling in C the terms of the various element submatrices C e ( e =1,2, … , N e , N e being the total number of elements) (Zienkiewicz and Taylor, 1989; Settanni et al , 1989). The calculation and assembly procedures can be carried out by resorting to the “matrix of the vertices” V which contains all information about the domain (Settanni et al , 1989). In the case of linear tetrahedral elements, this matrix has N e rows and four columns.…”

“…In order to reduce the memory employment, a row‐by‐row procedure which, working on the matrix of the vertices V , finds the non‐null terms of each row of C was suggested in Settanni et al (1989). But this procedure has turned out to be long, especially for 3D problems.…”