In recent decades, finite element (FE) techniques have been extensively used for predicting effective properties of random heterogeneous materials. In the case of very complex microstructures, the choice of numerical methods for the solution of this problem can offer some advantages over classical analytical approaches, and it allows the use of digital images obtained from real material samples (e.g., using computed tomography). On the other hand, having a large number of elements is often necessary for properly describing complex microstructures, ultimately leading to extremely time-consuming computations and high memory requirements. With the final objective of reducing these limitations, we improved an existing freely available FE code for the computation of effective conductivity (electrical and thermal) of microstructure digital models. To allow execution on hardware combining multi-core CPUs and a CPU, we first translated the original algorithm from Fortran to C, and we subdivided it into software components. Then, we enhanced the C version of the algorithm for parallel processing with heterogeneous processors. With the goal of maximizing the obtained performances and limiting resource consumption, we utilized a software architecture based on stream processing, event-driven scheduling, and dynamic load balancing. The parallel processing version of the algorithm has been validated using a simple microstructure consisting of a single sphere located at the centre of a cubic box, yielding consistent results. Finally, the code was used for the calculation of the effective thermal conductivity of a digital model of a real sample (a ceramic foam obtained using X-ray computed tomography). On a computer equipped with dual hexa-core Intel Xeon X5670 processors and an NVIDIA Tesla C2050, the parallel application version features near to linear speed-up progression when using only the CPU cores. It executes more than 20 times faster when additionally using the CPU. (C) 2012 Elsevier B.V. All rights reserved.