Solution of Potential Problems Using a Spectral Boundary Integral Method
MICHIGAN UNIV ANN ARBOR DEPT OF MECHANICAL ENGINEERING AND APPLIED MECHANICS
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The advantages of solving two-dimensional potential problems using spectral boundary integral methods are examined. Using fast Fourier transforms, we expand the spatial coordinates x and y using an arclength parameter s. This spectral representation is very accurate when the geometry is smooth and nodal spacing is uniform. Two spectral formulations are outlined. One is based on Bakers integration scheme at every other node to avoid the kernel singularities, and the other is based on the kernel desingularization of Roberts. An error analysis and convergence studies for several geometries are shown.
- Numerical Mathematics