A parallel RBF-VerBSS hybrid method for mesh deformation

Each chapter should be preceded by an abstract (no more than 200 words) that summarizes the content. The abstract will appear online at https://link.springer.com and be available with unrestricted access. This allows unregistered users to read the abstract as a teaser for the complete chapter. Please use the ‘starred’ version of the abstract command for typesetting the text of the online abstracts (cf. source file of this chapter template abstract) and include them with the source files of your manuscript. Use the plain abstract command if the abstract is also to appear in the printed version of the book. The mesh deformation method has been widely used in numerical simulation of time-variant problems. In this paper, we propose a hybrid mesh deformation method based on the radial basis functions (RBF) and vertex-ball-spring-smoothing (VerBSS) methods. Firstly, a background mesh, consistent with the boundary of the computational mesh, is generated and deformed by RBF. The internal nodal displacements are duplicated to the corresponding nodes of the computational mesh. The perturbated nodes and the boundary nodes are then utilized together to calculate the deformation of the computational mesh using VerBSS. Consequently, a better convergence performance is achieved. The results of the numerical examples show that the proposed method has higher efficiency and better robustness than the conventional RBF and background mesh methods, for large scale problems.