Error Propagation for Response Matrix Methods in the Many Node Limit

The response matrix method has been a useful solution method for radiation transport problems for decades. The method is desirable for many reasons. It can be extended to both fixed source and eigenvalue problems. In addition, a key aspect of the method is a shift of computational expense to a precomputation phase. Methods and codes employing response matrix or response matrix-like methods have enjoyed formidable computational efficiency while solving large problems. However, current applications of the method rely on large node sizes and few nodes to maximize computational efficiency. As part of a desire to make these methods more amenable to applications such as parallel computing in the future, the number of nodes in problems may increase, and node size will decrease. The effect of this change has not been well studied except for a few cases. In the past, it was determined that a poor approximation of angular dependence of flux on node interfaces could lead to large error propagation for fixed source problems, but a newer study indicates that changing node sizes as well as number of nodes poses little challenge for response methods in the eigenvalue case. This paper presents the unintuitive result that for response matrix methods increasing the spatial resolution of the problem may dramatically decrease accuracy - this effect is demonstrated on a simple analytic 1-D benchmark problem. (authors)