Treffer: The efficient element-free Galerkin method for 3D variable wave number Helmholtz equations.

In this study, we employed a strategy that integrates the dimension splitting method (DSM) with an improved element-free Galerkin (IEFG) method to develop an efficient element-free Galerkin (EEFG) approach. This innovative method was applied to solve the 3D variable wave number Helmholtz equations. By decomposing the 3D problem into a series of 2D and 1D subproblems, the IEFG method was effectively used to address the 2D plane problems. Simultaneously, the finite difference method (FDM) is employed for discretization. This approach has shown significant advantages in dealing with wave number variations within the 3D Helmholtz equations. Through the use of coupling techniques, we have substantially enhanced our ability to manage spatial variations in wave numbers, leading to a notable improvement in both the accuracy and efficiency of our numerical simulations. IMPACT STATEMENT The EEFG method proposed in this study for the 3D variable wave number Helmholtz equation significantly improves the solution efficiency and accuracy. The method has important applications in computational mechanics and engineering, especially in dealing with problems with complex boundary conditions and variable wave numbers. [ABSTRACT FROM AUTHOR]