Title :
Optimal finite-difference sub-gridding techniques applied to the Helmholtz equation
Author :
Nehrbass, John W. ; Lee, Robert
Author_Institution :
Supercomput. Center, Ohio State Univ., Columbus, OH, USA
fDate :
6/1/2000 12:00:00 AM
Abstract :
Since the spatial resolution of a uniform grid determines in part the accuracy of a given simulation, it must be judiciously chosen. In some small region of the computation domain, a fine grid density may be needed, while in the remainder of the domain, a coarser grid is acceptable. It would be preferable if a coarse resolution could be used over the majority of the computational domain, while locally using a finer resolution around the problem areas. In this presentation, a systematic method is presented that shows how to optimally choose the finite-difference coefficients for the transition region from a coarse to a fine grid. Results are presented for two-dimensional problems and for specific stencils. The ideas can then be applied to any dimension and any desired stencil in a straightforward manner. The sub-gridding methods are verified for accuracy through a study of scattering from curved geometries and propagation through dense penetrable materials
Keywords :
Helmholtz equations; electromagnetic wave propagation; finite difference methods; Helmholtz equation; coarse grid density; computation domain; curved geometries; dense penetrable materials; fine grid density; finite-difference coefficients; optimal finite-difference sub-gridding techniques; spatial resolution; stencils; sub-gridding methods; systematic method; two-dimensional problems; uniform grid; Computational modeling; Electromagnetic propagation; Electromagnetic scattering; Equations; Extrapolation; Finite difference methods; Geometry; Grid computing; Interpolation; Spatial resolution;
Journal_Title :
Microwave Theory and Techniques, IEEE Transactions on