A novel Mortar Method Integration using Radial Basis Functions

Abstract

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.