Efficient Construction of T-Mesh Bases via a Constraint Transformation Matrix
- 1School of Mechanical Engineering, National Technical University of Athens, 9 Iroon Polytechniou Str., 15780 Athens, Greece
Abstract
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.
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BibTeX
@article{provatidis2026efficient,
title = {{Efficient Construction of T-Mesh Bases via a Constraint Transformation Matrix}},
author = {Christopher G. Provatidis},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100763},
url = {https://www.mdpi.com/2075-1680/15/10/763},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Efficient Construction of T-Mesh Bases via a Constraint Transformation Matrix
AU - Christopher G. Provatidis
PY - 2026
DA - 2026/10/13
JO - Axioms
DO - 10.3390/axioms15100763
UR - https://www.mdpi.com/2075-1680/15/10/763
AB - 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.
SN - 2075-1680
ER -