Abstract: An automatic decomposition approach is proposed for 2D domains based on solving a vector field.It enables the automatic generation of high-quality block-structured quadrilateral meshes in arbitrary 2D domains.Firstly,a vector field that covers the entire problem domain is obtained by solving the Laplace-type governing equations with the boundary element method(BEM).The vector field also reflects the requirements of users on the generation of boundary aligned quadrilateral elements.Next,the vector field is converted into a frame field by using the basic map between these two fields.Finally,the problem domain is decomposed into several four-sided sub-regions by analyzing the singularities of the frame field,and a block-structured quadrilateral mesh is created by meshing the sub-regions individually with the mapping method.The effectiveness and reliability of the proposed method are verified with complex examples.