A parallel computation approach based on the properties of the Graphics Processor Units (GPU) is here presented to speed-up the broadband modeling of passive 3D structures. The full-wave electromagnetic model is based on a surface integral formulation, numerically implemented by using a null-pinv decomposition of the unknowns. The numerical model has been proven to be accurate and well-posed for a frequency range from DC to hundreds of GHz. A bottleneck of the model is the assembly of fully populated matrices and the final matrix inversion. This paper presents A GPU parallelization of the matrix assembly phase, and analyzes two case-studies which refer to full-wave analysis of interconnects. The achieved speedup with respect to a conventional serial approach is around 50x.