A novel mortar method integration using radial basis functions

Abstract

The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational grids for such problems often remains one of the main bottlenecks. The use of a domain partitioning with non-conforming grids is a possible solution, which, however, requires the development of robust and efficient inter-grid interpolation operators to transfer a scalar or a vector field from one domain to another. This work presents a novel approach for interpolating quantities across non-conforming meshes within the framework of the classical mortar method, where weak continuity conditions are enforced. The key contribution is the introduction of a novel strategy that uses mesh-free Radial Basis Function (RBF) interpolations to compute the mortar integral, offering a compelling alternative to traditional projection-based methods. We propose an efficient algorithm tailored for complex three-dimensional settings allowing for potentially significant savings in the overall computational cost and ease of implementation, with no detrimental effects on the numerical accuracy. The formulation, analysis, and validation of the proposed RBF-based algorithm is discussed with the aid of a set of numerical examples, demonstrating its effectiveness. Furthermore, the details of the implementation are discussed and a test case involving a complex geometry is presented, in order to illustrate the applicability and advantages of our approach in real-world problems.