Abstract
The surface integral equation (SLE) is used for induction well-logging modeling. The induction tools operate at very low frequencies, and very fine meshes comparable to wavelength are needed to accurately model the structure. To solve the low frequency breakdown problem of the EFIE operator, loop-tree or loop-star basis functions are necessary. To obtain a smaller number of iterations, basis rearrangement is used to lower the condition number of the matrix. We apply the contact-region-modeling (CRM) scheme on this problem and take the structure as a composite object. If we assume that the invasion zone is a single object, it is not a simply connected region anymore. A new kind of loop basis will emerge and need special treatment. After all these works, a fast algorithm can be applied to this problem for O(N) complexity.
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