  In the immersed boundary (IB) approach to fluid-structure interaction
modeling, the coupling between the fluid and structure variables is mediated
using a regularized version of Dirac delta function. In the IB literature, the
regularized delta functions, also referred to IB kernel functions, are either
derived analytically from a set of postulates or computed numerically using the
moving least squares (MLS) approach. Whereas the analytical derivations
typically assume a regular Cartesian grid, the MLS method is a meshless
technique that can be used to generate kernel functions on complex domains and
unstructured meshes. In this note we take a viewpoint that IB kernel
generation, either analytically or via MLS, is a constrained quadratic
minimization problem. The extremization of a constrained quadratic function is
a broader concept than kernel generation, and there are well-established
numerical optimization techniques to solve this problem. For example, we show
that the constrained quadratic minimization technique can be used to generate
one-sided (anisotropic) IB kernels and/or to bound their values.
