Numerical analysis of coupled heat and moisture transport in masonry

Coupled analysis of heat and moisture transport in real world masonry structures deserves a special attention because the spatial discretization by the finite element method leads usually to large number of degrees of freedom. Thin mortar layers and large bricks or stones have very different material properties and the finite element mesh has to be able to describe correct temperature and moisture fields in mortar and in its vicinity in the blocks. This paper describes two possible solutions of such problems. The first solution is based on the domain decomposition method executed on parallel computers, where the Schur complement method is used with respect to non-symmetric systems of algebraic equations. The second alternative method is the application of a multi-scale approach in connection with a processor farming method, where the whole structure is described by a reasonably coarse finite element mesh, called the macro-scale problem, and the material parameters are obtained from the lower-level problems, called the meso-scale problem, by a homogenization procedure. In this procedure, the macro-problem is assigned to the master processor and the meso-scale problems belong to the slave processors in the processor farm.