In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is t...In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is transformed into a boundary value problem with coupled boundary conditions.In numerical analysis,the perfectly matched layer(PML)and transparent boundary condition(TBC)are introduced to truncate the unbounded domain.Then,a linear gradient is constructed in a node-based smoothing domain(N-SD)by using a complete order of polynomial.The unknown coefficients of the smoothed linear gradient function can be solved by three linearly independent weight functions.Further,based on the weakened weak formulation,a system of linear equation with the smoothed gradient is established for NS-FEM-L with PML or TBC.Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy.It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness matrix,which effectively overcomes the instability of original NS-FEM.Moreover,the convergence rates of L 2 and H1 semi-norm errors for the two NS-FEM-L models are also higher.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11901423,12002290 and 11771321)the Youth Science and the Technology Research Foundation of Shanxi Province(Grant Nos.201901D211104 and 201901D211107)the Shanxi Youth Top-Notch Talent Support Program(Grant No.DT18100306).
文摘In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is transformed into a boundary value problem with coupled boundary conditions.In numerical analysis,the perfectly matched layer(PML)and transparent boundary condition(TBC)are introduced to truncate the unbounded domain.Then,a linear gradient is constructed in a node-based smoothing domain(N-SD)by using a complete order of polynomial.The unknown coefficients of the smoothed linear gradient function can be solved by three linearly independent weight functions.Further,based on the weakened weak formulation,a system of linear equation with the smoothed gradient is established for NS-FEM-L with PML or TBC.Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy.It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness matrix,which effectively overcomes the instability of original NS-FEM.Moreover,the convergence rates of L 2 and H1 semi-norm errors for the two NS-FEM-L models are also higher.
