Development of Domain Decomposition Method with Meshless Virtual Nodes: Verification of Method and Parallel Performance Evaluation

A high-performance domain decomposition method (MVDDM) is proposed for the parallel finite element analysis using meshless virtual nodes along the domain interface. The domains, which are analyzed independently in parallel by the finite element method, are connected by the virtual nodes based on the moving least squares method. The conjugate gradient method is applied to the virtual nodes to obtain the solution on the domain interface. To verify this method, various two-dimensional problems are solved. The accuracy of the solutions are good enough for practical use, and the convergence of the conjugate gradient method and the parallel performance are improved with fewer virtual nodes. This method can be applied to the problem with non-conforming interface among domains. This method can also accelerate the convergence of the CG method.