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The boundary integral equation (BIE) method was first proposed by Yan and Sakurai (2000) and used to extrapolate the nonlinear force‐free magnetic field in the solar atmosphere. Recently, Yan and Li (2006) improved the BIE method and proposed the direct boundary integral equation (DBIE) formulation, which represents the nonlinear force‐free magnetic field by direct integration of the magnetic field on the bottom boundary surface. On the basis of this new method, we devised a practical calculation scheme for the nonlinear force‐free field extrapolation above solar active regions. The code of the scheme was tested by the analytical solutions of Low and Lou (1990) and was applied to the observed vector magnetogram of solar active region NOAA 9077. The results of the calculations show that the improvement of the new computational scheme to the scheme of Yan and Li (2006) is significant, and the force‐free and divergence‐free constraints are well satisfied in the extrapolated fields. The calculated field lines for NOAA 9077 present the X‐shaped structure and can be helpful for understanding the magnetic configuration of the filament channel as well as the magnetic reconnection process during the Bastille Day flare on 14 July 2000.

Nonlinear force‐free coronal magnetic field extrapolation scheme based on the direct boundary integral formulation