The geometric characteristics of the convex optical element in the magnetorheological polishing area have an important influence on the manufacture of high precision and high surface integrity optical elements.Variations in curvature,embedding depth and angle of the convex optical element will cause the change of pressure field in the magnetorheological polishing area.In order to study the pressure field of the polishing area under different curvatures,embedding depths and embedding angles of convex optical elements,the pressure in the polishing area was analyzed firstly by establishing a pressure model during the magnetorheological polishing process.Secondly,a fast calculation method for multi field coupled integral was established based on the Kahan numerical method.Finally,the pressure field distribution of the magnetorheological polishing area is obtained by calculating the convex optical element under different curvatures,embedding depths and angles,and the process law of the convex element affected by the geometric characteristics in the magnetorheological polishing area is studied.It is concluded that in the polishing process,by changing the curvature of the convex optical element,the embedding depth and the angle under the same curvature,when the curvature of the processed convex element increases,the pressure field of the magnetorheological polishing area will increase accordingly；when the curvature of the convex element is constant and the embedding depth gradually deepens,the pressure field of the magnetorheological polishing area will increase；when the curvature of the convex element is constant and the embedding angle increases,the pressure field of the magnetorheological polishing area will increases and then decreases with the angle.