Identify a separable function space for reciprocal B-spline approximation

Identify a separable linear function space that is well suited for approximating reciprocals of B-spline functions, particularly reciprocal determinants arising in the stiffness-tensor assembly for orientation-preserving tensor-product B-spline geometries.

Background

The stiffness-tensor construction requires approximating the reciprocal determinant $\rho=1/\omega$, where $\omega$ is the determinant of the Jacobian of an orientation-preserving tensor-product B-spline geometry map. Although $\omega$ is a spline function, its reciprocal is generally rational and therefore does not belong to a non-rational B-spline space.

The paper projects $\rho$ onto a tensor-product B-spline space to obtain a separable low-rank representation, but notes that no generally suitable separable linear approximation space is known. Developing such a space could improve the accuracy and reduce the computational cost of the projection-based stiffness assembly by requiring fewer basis functions than generic tensor-product spline spaces.