A Hybrid GNN approach for predicting node data for 3D meshes

Metal forging is used to manufacture dies. We require the best set of input parameters for the process to be efficient. Currently, we predict the best parameters using the finite element method by generating simulations for the different initial conditions, which is a time-consuming process. In this paper, introduce a hybrid approach that helps in processing and generating new data simulations using a surrogate graph neural network model based on graph convolutions, having a cheaper time cost. We also introduce a hybrid approach that helps in processing and generating new data simulations using the model. Given a dataset representing meshes, our focus is on the conversion of the available information into a graph or point cloud structure. This new representation enables deep learning. The predicted result is similar, with a low error when compared to that produced using the finite element method. The new models have outperformed existing PointNet and simple graph neural network models when applied to produce the simulations

Superlinear convergence using block preconditioners for the real system formulation of complex Helmholtz equations

International audienceComplex-valued Helmholtz equations arise in various applications, and a lot of research has been devoted to finding efficient preconditioners for the iterative solution of their discretizations. In this paper we consider the Helmholtz equation rewritten in real-valued block form, and use a preconditioner in a special two-by-two block form. We show that the corresponding preconditioned Krylov iteration converges at a mesh-independent superlinear rate