Keywords: heat and moisture transfer, homogenization, masonry, periodic unit cell, finite element method, parallel computing.

Numerical modelling of coupled heat and moisture transport in masonry using the finite element method leads to huge number of degrees of freedom. This is caused mainly by an effort to create a suitable finite element mesh in the mortar between stones and their vicinity in order to capture the correct temperature and moisture distribution. Such problems with too many degrees of freedom are hardly solvable on single processor computers. One of possible solutions of the mentioned difficulties is an application of a multi-scale approach. This paper presents a hybrid parallel method based on multi-scale analysis. In the hybrid method, each macro-scopic integration point or each finite element is connected with a certain meso-scopic problem represented by an appropriate periodic unit cell. The solution of a meso-scale problem then provides effective parameters needed on the macro-scale. Such an analysis is suitable for parallel computing because the meso-scale problems can be distributed among many processors and the amount of transferred data is small. In this regard, the master-slave strategy can be efficiently exploited. Results of the computation are illustrated using a numerical analysis of the coupled heat and moisture transfer in the Charles Bridge in Prague.

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