In the context of multi-physics simulations on unstructured and heterogeneous meshes, generating well-balanced partitions is not trivial. The computing cost per mesh element in different phases of the simulation depends on various factors such as its type, its connectivity with neighboring elements or its layout in memory with respect to them, which determines the data locality. Moreover, if different types of discretization methods or computing devices are combined, the performance variability across the domain increases. Due to all these factors, evaluate a representative computing cost per mesh element, to generate well-balanced partitions, is a difficult task. Nonetheless, load balancing is a critical aspect of the efficient use of extreme scale systems since idle-times can represent a huge waste of resources, particularly when a single process delays the overall simulation. In this context, we present some improvements carried out on an in-house geometric mesh par-titioner based on the Hilbert Space-Filling Curve. We have previously tested its effectiveness by partitioning meshes with up to 30 million elements in a few tenths of milliseconds using up to 4096 CPU cores, and we have leveraged its performance to develop an autotuning approach to adjust the load balancing according to runtime measurements. In this paper, we address the problem of having different load distributions in different phases of the simulation, particularly in the matrix assembly and in the solution of the linear system. We consider a multi-partition approach to ensure a proper load balance in all the phases. The initial results presented show the potential of this strategy.