Daniele Moretto, Andrea Franceschini, Massimiliano Ferronato
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A novel Mortar Method Integration using Radial Basis Functions
Recent advancements in computational capabilities have significantly enhanced
the numerical simulation of complex multiphysics and multidomain problems.
However, mesh generation remains a primary bottleneck in these simulations. To
address this challenge, non-conforming grids are often utilized, which
necessitates the development of robust and efficient intergrid interpolator
operators. This paper presents a novel approach for transferring variable
fields across non-conforming meshes within a mortar framework, where weak
continuity conditions are imposed. The key contribution of our work is the
introduction of an innovative algorithm that utilizes Radial Basis Function
(RBF) interpolations to compute the mortar integral, offering a compelling
alternative to traditional projection-based algorithms. Pairing RBF methods
with numerical integration techniques, we propose an efficient algorithm
tailored for complex three-dimensional scenarios. This paper details the
formulation, analysis, and validation of the proposed RBF algorithm through a
series of numerical examples, demonstrating its effectiveness. Furthermore, the
details of the implementation are discussed and a test case involving a complex
geometry is presented, to illustrate the applicability and advantages of our
approach in addressing real-world problems.