Solving fully-coupled non-linear hygro-thermo-mechanical problems relative to the behavior of concrete at high temperatures is nowadays a very interesting and challenging computational problem. These models require an extensive use of computational resources, such as main memory and computational time, due to the great number of variables and the numerical characteristics of the coefficients of the linear systems involved. In this paper a number of different variants of a frontal solver used within HITECOSP, an application developed within the BRITE Euram III "HITECO" EU project, to solve multiphase porous media problems, are presented, evaluated and compared with respect to their numerical accuracy and performance. The final result of this activity is a new solver which is both much faster and more accurate than the original one. Specifically, the code runs over 5 times faster and numerical errors are reduced of up to three order of magnitude.