Mesh deformation using the biharmonic operator

By B. Helenbrook. 2003

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Unified fluid–structure interpolation and mesh motion using radial basis functions (2008, background): “Grid quality can be improved by solving a bi-harmonic set of equations that also preserve orthogonality [41, 42].”
Fluid-structure interactions using different mesh motion techniques (2011, methodology): “As a third approach, we use the biharmonic operator for deforming the mesh with two types of boundary conditions [12].”
Aircraft control surface deflection using RBF‐based mesh deformation (2011, background): “[15, 25]), but all field points have to be considered.”
Automatic mesh motion for the unstructured finite volume method (2007, methodology): “Notably, in an effort to simultaneously control the position of the free boundary and mesh spacing next to it, Helenbrook [23] proposes the use of a biharmonic equation to govern mesh motion.”
Unrestricted Facial Geometry Reconstruction Using Image-to-Image Translation (2017, background): “where, wi,j is the weight corresponding to the biharmonic Laplacian operator (see [21, 5]), ~n(ci) is the”