By J. E. Akin
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Extra resources for Application and Implementation of Finite Element Methods (Computational Mathematics and Applications)
Next it reads the element number and the element incidences (node numbers of all nodal points associated with the element) for every element in the system. These data are also printed for the purpose of checking the input data. Given the number of nodes, number of elements, the number of nodes per element, number of parameters per node, and the dimensions of the space, this subroutine sets aside storage for the spatial coordinates, element incidences, and the nodal point boundary code indicator.
In an integral formulation involving a Neumann-type boundary condition the boundary flux contributions usually define a column matrix, say Cb, with NFLUX coefficients and a corresponding square matrix. These matrices are often defined by integrals of the form = Sb = f HIHbP ds, where f denotes the specified flux components, P = P(f) is a coefficient defined on the boundary, and Hb represents the element interpolation functions along that boundary segment. If the flux components and the parameter of interest both vary linearly along the element boundary segment, one obtains (as shown later) a boundary column matrix contribution such as the one shown in Fig.
These elementary operations are executed by subroutine ELBAND, which is shown in Fig. 3, and they are based on Fig. 4. The simple but important task of determining the value of the maximum half-bandwidth of the system equations is performed by subroutine SYSBAN, Fig. 5. The half-bandwidth of each element is checked and the largest value found in the system is retained. The system equations usually occupy a very large percentage of the total storage. Knowing the system equation's half-bandwidth, determined above, and the total numbers of 37 3.