Different from the way we have been looking in the past at developments encompassing modal type and a wide class of step-by-step time stepping approaches for transient and dynamic field problems, and significantly different from the way these have been developed and described in standard text books over the years, this paper outlines the theoretical ideas and basis towards providing a generalized methodology and formulations leading to integral and a wide class of integration operators for the resulting solution of these transient equation systems. It is herein postulated that integral operators and a wide class of integration operators pertain to and emanate from the same family, with the burden which is being carried by a virtual field or weighted function field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi-discretized equation system. Subsequently, the selection or burden carried by the virtual or weighted function fields originally introduced to facilitate the time discretization process determines the formal development and outcome of 'exact integral operators', 'approximate integral operators', and a wide class of 'integration operators'. Thus, the present developments not only serve as a prelude towards the formal developments for 'exact integral operators', but also demonstrate that the resulting 'approximate integral operators' and a wide class of 'integration operators and known methods' are simply subsets of the generalizations of a standardized Wp-Family, and emanate from the principles presented herein. The burden of weight and the resulting consequences towards subsequently enabling a formal basis for the selection of discrete numerically assigned [DNA]-algorithmic markers to particularly identitfy a wide class of algorithms is described for transient field problems and dynamic field problems, respectively.
|Original language||English (US)|
|Number of pages||36|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|State||Published - Oct 1997|