Abstract
In this work, we apply a recently developed theory, information-based complexity, to numerical transport theory. Two classes of information, cell-average information and point-evaluation information, and two popular algorithms, the step-characteristics and diamond-differences, are discussed in view of information-based complexity, for a one-dimensional model problem. For this problem, optimal errors and algorithms for these two types of information are presented, and we also show that the diamond-difference method always has a smaller worst-case error than the step-characteristic method, when both use the same cell-average information. For a model problem in two-dimensional transport, we obtain the radius of the cell-average information, which is the optimal (worst-case) error. The corresponding central algorithm that possesses this optimal error is developed. Further, we theoretically and numerically compare four algorithms, the step-characteristic, diamond-difference, (C, C) nodal transport, and corner-balance algorithms, for a single cell. A number of figures and a table are presented for those comparisons. Such results allow the best choice of algorithm to solve the model problem, depending on the angular variables (μ, η) and cell width h.
Yu, Fan (1992). Information-based complexity applied to numerical transport theory. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1348974.