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A 3-D coronal magnetic field is reconstructed for NOAA 11158 on Feb 14, 2011.A GPU-accelerated direct boundary integral equation (DBIE) method isimplemented. This is about 1000 times faster than the original DBIE used onsolar NLFFF modeling. Using the SDO/HMI vector magnetogram as the bottomboundary condition, the reconstructed magnetic field lines are compared withthe projected EUV loop structures from different views three-dimensionally bySDO/AIA and STEREO A/B spacecraft simultaneously for the first time. They showvery good agreement so that the topological configurations of the magneticfields can be analyzed, thus its role in the flare process of the active regioncan be better understood. A quantitative comparison with some stereoscopicallyreconstructed coronal loops shows that the present averaged misalignment anglesare at the same order as the state-of-the-art results obtained withreconstructed coronal loops as prescribed conditions and better than otherNLFFF methods. It is found that the observed coronal loop structures can begrouped into bundles of closed and open loops with some central bright coronalloops around the polarity inversion line (PIL). The reconstructedhighly-shearing magnetic field lines agree very well with the low-lyingS-shaped filament channel along PIL. They are in a pivot position to all othersurrounding coronal structures, and a group of electric current linesco-aligned with the central bright EUV loops overlying the filament channel isalso obtained. This central lower-lying magnetic field loop system must haveplayed a key role in powering the flare. It should be noted that while astrand-like coronal feature along PIL may be related to the filament, onecannot simply attribute all the coronal bright features along PIL tomanifestation of the filament without any stereoscopically information. Itshows that DBIE is rigorous and effective.

3-D nonlinear force-free field reconstruction of solar active region 11158 by direct boundary integral equation