An alternative method for degenerate scale problems in boundary element methods for the two-dimensional Laplace equation |
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| Affiliation: | 1. CEMAT-IST, Universidade de Lisboa, Av. Rovisco Pais 1, Lisbon 1049-001, Portugal;2. GFM-FCUL, Universidade de Lisboa, Campo Grande C6, Lisboa 1749-016, Portugal;1. Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan;2. Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan;3. Bachelor Degree Program in Ocean Engineering and Technology, National Taiwan Ocean University, Keelung 20224, Taiwan;4. Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan;5. Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung, Taiwan |
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| Abstract: | The boundary integral equation approach has been shown to suffer a nonunique solution when the geometry is equal to a degenerate scale for a potential problem. In this paper, the degenerate scale problem in boundary element method for the two-dimensional Laplace equation is analytically studied in the continuous system by using degenerate kernels and Fourier series instead of using discrete system using circulants Engng Anal. Bound. Elem. 25 (2001) 819]. For circular and multiply-connected domain problems, the rank-deficiency problem of the degenerate scale is solved by using the combined Helmholtz exterior integral equation formulation (CHEEF) concept. An additional constraint by collocating a point outside the domain is added to promote the rank of influence matrix. Two examples are shown to demonstrate the numerical instability using the singular integral equation for circular and annular domain problems. The CHEEF concept is successfully applied to overcome the degenerate scale and the error is suppressed in the numerical experiment. |
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