FINITE ELEMENT ANALYSIS METHOD UTILIZING A BANDWIDTH MAXIMIZED MATRIX

摘要

An improvement in the method of finite element analysis of a physical system increases the speed of solution in backsubstitution and forward elimination by removing the data dependencies that would otherwise force sequential calculations. This is accomplished by translating a system matrix into a decomposed triangular matrix (Fig 5B) having non-zero data on its diagonal and in its corners, separated by a preselected band (K) of zero-only data. Such a bandwidth maximized matrix is created by renumbering the nodes of the finite element mesh (or more precisely the row and column numbers of the unknowns associated with the nodes) so that the numbers assigned to adjacent nodes differ by a sufficient amount to create the above noted band. The matrix can be processed in a parallel processor (Fig 1), one cell 15 of which derives the values of elements in a vector of unknown quantities and supplies the values to other cells, the other cells 15 using these values to derive partial products which are supplied to the first cell, for use in deriving the values of further elements in the vector. IMAGE