Efficient Construction of T-Mesh Bases via a Constraint Transformation Matrix

This paper addresses the treatment of large T-elements, based on Lagrange interpolation, through the application of constraints along the horizontal and vertical mesh lines of a quadrilateral patch. Instead of resorting to manual or symbolic factorization to determine explicit closed-form expressions of the shape functions, we propose constructing a transformation matrix and applying it directly to the background tensor-product grid, thereby establishing a linear relationship between the active (primary or master) and the auxiliary (secondary or slave) degrees of freedom. Software implementation is greatly simplified when all data (boundary conditions, slave-node definitions, etc.) refer directly to the background tensor-product mesh, while the subsequent computation of the corresponding nodal values streamlines post-processing operations. Representative numerical examples illustrate the correctness of the proposed formulation and demonstrate its practical effectiveness in the analysis of field, elasticity and eigenvalue problems.