Barycentric basis functions on mixed triangular-quadrilateral meshes for integral equations

New quadrilateral barycentric meshes (QBMs) are introduced for mixed triangular/quadrilateral discretizations in solving surface integral equations. By dividing a triangle into three quadrilaterals and a quadrilateral into four quadrilaterals, new original- and dual- basis functions (BFs) are defined where the building-blocks are quadrilateral edge BFs on QBMs. The QBM BFs require a small number of unknowns with low computational time and memory costs. Numerical examples validate the performances of the proposed BFs.