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IEEE Transactions on Microwave Theory and Techniques
Volume 48 Number 6, June 2000

Table of Contents for this issue

Complete paper in PDF format

Optimal Finite-Difference Sub-Gridding Techniques Applied to the Helmholtz Equation

John W. Nehrbass, Member, IEEE and Robert Lee Member, IEEE

Page 976.

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.

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