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Self-consistently solving the Schrödinger and Poisson's equations in the six-band k.p context can yield the valence-band structure in the inversion layers of pMOSFETs. In this numerically demanding process, the central processing unit (CPU) time is extraordinarily long. To overcome the hurdle, we construct a novel computational accelerator to intrinsically boost a self-consistent six-band k.p simulation. This accelerator comprises a triangular-potential-based six-band k.p simulator, a hole effective mass approximation (EMA) technique, and an electron analogy version of the self-consistent Schrödinger and Poisson's equations solver. The outcome of the accelerator furnishes the initial solution of the confining electrostatic potential and is likely close to the realistic one, which is valid for different temperatures, substrate doping concentrations, inversion hole densities, and surface orientations. The results on (001) and (110) substrates are supported by those published in the literature. The overall CPU time is reduced down to around 8% of that without the accelerator. This is the first successful demonstration of the EMA in the self-consistent hole subband structure calculation. The application of the proposed accelerator to more general situations is projected as well.