A new numerical scheme using a renormalization and a 3D boundary integral equation method is proposed to simulate a multi-scaling dynamic rupture of earthquakes: How a small earthquake grows up to a large one in spatially heterogeneous field of critical slip-weakening distance Dc (fracture energy Gc)? We examine the case where Dc grows according to a hypocentral distance L (Dc ∝ L¿). When ¿ = 1, we succeed to show numerically that a rupture propagates at a constant rupture speed in uniform initial stress field. This result still keeps the scaling relation of Gc and Dc inferred for earthquake size, however no scale-dependent initial process is required. The break of the proportional relation changes rupture speed as well as slip velocity to keep the energy balance. The rupture is accelerated up to a speed even faster than the shear wave velocity (¿ 1).