Efficient cubature rules for the numerical integration of logarithmic singularities
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Date
2014
Publication Type
Conference Paper
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yes
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Abstract
In this work, we aim to improve the efficiency of a higher-order boundary element method for solving axi-symmetric electrostatic problems. To do so, we generate a set of tailored two-dimensional cubature rules for the efficient numerical integration of logarithmic singularities. In a series of numerical experiments, we demonstrate that our cubature rules can reduce the matrix setup time by a factor of two when compared to a more conventional tensor-product approach. This allows a significant reduction in computational time for the reconstruction of dielectric properties in Near-Field Scanning Microwave Microscopy. Furthermore, our approach is by no means limited to axi-symmetric systems or logarithmic singularities. The procedure can be readily generalized to the four-dimensional integrals occurring in fully three-dimensional computations and it can also be modified to handle stronger singularities.
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published
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Book title
2014 International Conference on Electromagnetics in Advanced Applications (ICEAA)
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Volume
Pages / Article No.
601 - 604
Publisher
IEEE
Event
16th International Conference on Electromagnetics in Advanced Applications (ICEAA 2014)