Abstract
This work deals with numerical techniques to compute electrostatic fields in devices with rounded corners in 2D situations. The approach leads to the solution of two problems: one on the device where rounded corners are replaced by sharp corners and the other on an unbounded domain representing the shape of the rounded corner after an appropriate rescaling. Both problems are solved using different techniques and numerical results are provided to assess the efficiency and the accuracy of the techniques.
Highlights
The precise description of an object containing rounded corners leads to consider meshes with a large number of nodes in the corner neighborhood when the finite element method (FEM) is straightforwardly applied
With a reduced amount of numerical computations it is possible to determine the variation of the electric field close to the rounded corner as a function of the curvature radius
The value of max(|E∞|) is 1.147 V/m
Summary
The precise description of an object containing rounded corners leads to consider meshes with a large number of nodes in the corner neighborhood when the finite element method (FEM) is straightforwardly applied. Dealing with such meshes makes the computation time- and resourceconsuming. These computations have to be repeated if the curvature radius of the rounded corner is modified. The exact solutions close to the corner, computed for several values of the curvature radius ε, are quasi-similar, up to a “scaling factor” (related to ε). Principles of the method For the sake of clarity, the method is explained on a specific structure, see Fig. 1, but it can be straightforwardly extended to other structures, in particular including more than two electric conductors
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