| Abstract: Radiation and magnetic fields play essential roles in understanding accretion physics around neutron stars and black holes, particularly in near- and super-Eddington regimes. For black hole accretion in the near-Eddington regime, the disk structure depends on the initial magnetic field topology, allowing for the formation of thin disks with magnetic coronae or magnetically elevated disks. In the super-Eddington regime, the radiation-supported disk undergoes thermal expansion but is constrained by the magnetic tension of helical fields along the jet sheath, which shapes a conical funnel in the outflow region. For accretion onto a strongly magnetized neutron star, the magnetic field disrupts the disk structure, channeling accretion flows along field lines toward the magnetic poles. At sufficiently high accretion rates, radiation pressure supports this magnetically confined flow, forming a column structure near the poles. To model these processes, we solve (general) relativistic MHD equations coupled with angle-dependent radiation transfer, allowing us to capture the dynamics driven by radiation and magnetic fields in extreme environments. Our simulation results align with several observational findings and provide predictive diagnostics for future observations. |