Fast ignition (FI) is investigated via integrated particle-in-cell simulation including both generation and transport of fast electrons, where petawatt ignition lasers of 2 ps and compressed targets of a peak density of 300 g cm(-3) and areal density of 0.49 g cm(-2) at the core are taken. When a 20 MG static magnetic field is imposed across a conventional cone-free target, the energy coupling from the laser to the core is enhanced by sevenfold and reaches 14%. This value even exceeds that obtained using a cone-inserted target, suggesting that the magnetically assisted scheme may be a viable alternative for FI. With this scheme, it is demonstrated that two counterpropagating, 6 ps, 6 kJ lasers along the magnetic field transfer 12% of their energy to the core, which is then heated to 3 keV.