Spectral method for matching exterior and interior elliptic problems

摘要: A spectral method is described for solving coupled elliptic problems on an interior and exterior domain. The formulated tested the two-dimensional Poisson Laplace problems, whose solutions their normal derivatives are required to be continuous across interface. complete basis of homogeneous regions, corresponding all possible Dirichlet boundary values at interface, calculated in a preprocessing step. This used construct influence matrix which serves transform conditions into problem. Chebyshev approximations represent both values. standard calculate solutions. harmonic as convolution free-space Green's function with surface density; this density itself solution integral equation has analytic when given expansion. Properties insure that functions represents external near-boundary uniformly. by calculating electrostatic potential resulting from charge distributions rectangle. well-conditioned converge exponentially resolution increased. generalization approach three-dimensional discussed, particular magnetohydrodynamic equations finite cylindrical domain surrounded vacuum.