We present in this paper the results of a research motivated by the need of a very fast solution of thermal flow in solar receivers. These receivers are composed by a large number of parallel pipes with the same geometry. We have introduced a reduced Schwarz algorithm that skips the computation in a large part of the pipes. The computation of the temperature in the skep domain is replaced by a reduced mapping that provides the transmission conditions. This reduced mapping is computed in an off-line stage. We have performed an error analysis of the reduced Schwarz algorithm, proving that the error is bounded in terms of the linearly decreasing error of the standard Schwarz algorithm, plus the error stemming from the reduction of the trace mapping. The last error is asymptotically dominant in the Schwarz iterative process. We obtain $L^2$ errors below $2\%$ with relatively small overlapping lengths.

翻译：本文介绍了一项旨在满足太阳能接收器中热流快速求解需求的研究成果。这些接收器由大量几何形状相同的平行管道组成。我们提出了一种简化施瓦兹算法，该算法能跳过大部分管道的计算。跳过区域内的温度计算被替换为一个提供传输条件的简化映射。该简化映射在离线阶段完成计算。我们对简化施瓦兹算法进行了误差分析，证明其误差受限于标准施瓦兹算法的线性递减误差与迹映射简化引入的误差之和，其中后者在施瓦兹迭代过程中渐近占主导地位。在相对较小的重叠长度下，我们实现了低于2%的$L^2$误差。