USING PINN TO SOLVE EQUATIONS OF EQUIDISTRIBUTIONAL METHOD FOR CONSTRUCTING 2D STRUCTURED ADAPTED NUMERICAL GRIDS

Abstract

The Equidistributional method is a popular technique for constructing numerical grids in engineering and scientific simulations. It is based on the principle of equidistribution, which requires evenly spaced grid points to reduce numerical errors. However, traditional Equidistributional methods can become inefficient and inaccurate for complex geometries and boundary conditions. In this paper, we present a new approach for solving the Equidistributional method's equations using physics-informed neural networks (PINN). PINN is a type of machine learning algorithm that has been shown to be effective for solving partial differential equations (PDEs). Our findings suggest that the use of PINN has the potential to significantly enhance the performance of the Equidistributional method for constructing 2D structured adapted numerical grids.