It is then integrated into a Fourier spectral moving mesh method, using the parabolic Monge Ampère equation for mesh control.
Numerical examples using the new adaptive moving mesh semi-implicit Fourier spectral method are presented for both two and three space dimensional microstructure simulations, and they are compared with those obtained by other methods.
This work extends the machinery of the moving mesh partial differential equation (MMPDE) method to the spectral collocation discretization of time-dependent partial differential equations.
In this paper, we report our recent progress in making grid points spatially adaptive in the physical domain via a moving mesh strategy, while maintaining a uniform grid in the computational domain for the spectral implementation.
Moreover, the error for the moving mesh is smaller than that for fixed (uniform) mesh.
Both cases, with a uniform mesh and with a moving mesh, are tested.
The moving mesh function (x xi,t)) satisfies certain parabolic equations which are called moving mesh partial differential equations (MMPDEs).
Moving mesh partial differential equations (MMPDEs) are used in the MMPDE moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems.
This feature allows the usage of a moving mesh easily.
