  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.
