A boundary-oriented reduced Schwarz domain decomposition technique for parametric advection-diffusion problems

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.