A NOTE OF INVERTIBLE TWO-DIMENSIONAL QUADRATIC FINITE ELEMENT TRANSFORMATIONS.

This paper presents a simple algorithm for verifying the non-singularity of parametric transformations with quadratic Jacobian determinants. The method is suitable for such transformations applied to all convex polygonal two-dimensional master-elements, but emphasis is placed on the triangle and the square. Geometric insight is used to curtail testing procedures where possible. The algorithm is compared for efficiency to a related procedure in which no use is made of the geometry of the implied curves. Results indicate that the geometric procedure, while slower in some cases owing to additional tests, is considerably more efficient for those cases where the geometry allows early termination of the algorithm. [ABSTRACT FROM AUTHOR]