EFFICIENT MESH DEFORMATION BASED ON RANDOMIZED RBF SOLVERS
Résumé
Mesh deformation methods have been widely used for the past decades in various fields
such as fluid-structure interaction, aerodynamic shape optimization, unsteady and aeroelastic
computational fluid dynamics. Among the existing methods, radial basis functions
interpolation (RBF) [1] is particularly suitable for unstructured mesh applications due to
its simplicity and the high quality of the resulting mesh. Such approach requires solving
dense linear systems, generally symmetric positive definite (SPD), which tends to be computationally
expensive and memory demanding, which is a major drawback when dealing
with large-scale meshes [2, 3].
In this work, we aim to speed-up RBF mesh deformation procedure using methods coming
from probabilistic linear algebra to solve the associated dense linear system. Indeed,
such methods start to emerge into several fields, including numerical linear algebra and
optimization [4], exploiting its spectral properties as an efficient alternative to reduce the
complexity of solving large scale linear system. We will address the question of how to
create an approximation to the RBF matrix by projecting the initial large scale operator
onto a smaller subspace that exhibits specific properties such as a better sparsity and
investigate various solving strategies.
The proposed approach will be discussed on the basis of 2D and 3D applications.