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In the immersed boundary (IB) approach to fluid-structure interactionmodeling, the coupling between the fluid and structure variables is mediatedusing a regularized version of Dirac delta function. In the IB literature, theregularized delta functions, also referred to IB kernel functions, are eitherderived analytically from a set of postulates or computed numerically using themoving least squares (MLS) approach. Whereas the analytical derivationstypically assume a regular Cartesian grid, the MLS method is a meshlesstechnique that can be used to generate kernel functions on complex domains andunstructured meshes. In this note we take a viewpoint that IB kernelgeneration, either analytically or via MLS, is a constrained quadraticminimization problem. The extremization of a constrained quadratic function isa broader concept than kernel generation, and there are well-establishednumerical optimization techniques to solve this problem. For example, we showthat the constrained quadratic minimization technique can be used to generateone-sided (anisotropic) IB kernels and/or to bound their values.

On immersed boundary kernel functions: a constrained quadratic minimization perspective