Some numerical results using the modified Nyström method to solve the 2-D potential problem
✍ Scribed by R.S.-C. Cheng
- Book ID
- 103974910
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 671 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0955-7997
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✦ Synopsis
In this paper, the author uses the modified Nystr6m method on the boundary integral equation formulated by using the single-layer potential representation to solve two-dimensional potential problems in which the boundary condition is mixed and/or the domain has corners. For these problems, he either augments the single-layer potential representation with exceptional functions or uses a graded mesh. The modified Nystrtm method requires only O(n 2) arithmetic operations to formulate the matrices and is similar to the Nystrtm method, except the numerical difficulty in integrating the logarithmic kernel is overcome. He compares his approach numerically with three other approaches previously published. In comparison with using the Galerkin-collocation method on the boundary integral equation formulated by using Green's theorem, his approach requires fewer computations and obtains more accurate solutions, especially for small meshes. In comparison with using the Nystrtm method on the boundary integral equation formulated by using the double-layer potential representation, his approach obtains more accurate solutions away from the boundary. In comparison with using the extension-BEM method, his approach is more direct, but still obtains accurate interior solution using a small mesh.