Showing papers by "Nathan Ida published in 1984"

Solution of linear equations for small computer systems

Abstract: A solution technique, based on Gauss elimination, is described which can solve symmetric or unsymmetric matrices on computers with small core and disk requirement capabilities. The method is related to frontal techniques in that renumbering of the nodes, such as in a finite element mesh, is not required, and the elimination is performed immediately after the equations for a particular node have been fully summed. Only two rows of the matrix need be on core at any step of the solution, but for more efficiency, the program presented here requires all the equations associated with two nodes to be on core. Minimum disk storage is achieved by storing only nonzero entries of the matrix, a single pointing vector for each node, regardless of the number of degrees-of-freedom, and the use of a single sequential file. Special care is taken of the boundary nodes where only the diagonal and the right-hand-side vector are stored. Assembly and elimination for these nodes are avoided completely. The performance of the program is compared with both symmetric and nonsymmetric frontal routines and is shown to be acceptable. The major merit of the method lies in the fact that it can be implemented on small minicomputers. The reduction of core and disk storage inevitably increases the solution time, but the decrease in the output file size also makes the back-substitution and resolution processes more efficient. In some cases, the total solution time can be shorter than for the frontal method due to this property.

Development of A 3-D Eddy Current Model for Nondestructive Testing Phenomena

Abstract: The success of two-dimensional eddy current models for modeling a variety of important nondestructive testing situations has been reported elsewhere1-3. These models, based on the finite element method, are limited to two-dimensional and axisymmetric geometries but, nevertheless are quite capable of providing important data for many practical test geometries which can be approximated by 2-D or axisymmetric formulations. The general NDT problem, is, however, a true three-dimensional problem and must be modeled as such. A 3-D eddy current model is, therefore, a natural and obvious extension of the 2-D modeling capabilities available today. Such a model is particularly valuable since the interaction between applied fields, induced currents and complicated material discontinuities cannot be described by closed form equations nor can they be approximated by 2-D geometries. In addition, such situations cannot be replicated experimentally and, therefore, the numerical model is in many cases the only practical way to provide training data for signal processing equipment and algorithms and indeed, the only way to determine defect characterization parameters to aid in the design of eddy current probes and testing equipment.