A spectral embedding method applied to the advection-diffusion equation
Journal of Computational Physics
Exponential convergence of a linear rational interpolant between transformed Chebyshev points
Mathematics of Computation
Free vibration analysis of curvilinear quadrilateral plates by the differential quadrature method
Journal of Computational Physics
A Rational Spectral Collocation Method with Adaptively Transformed Chebyshev Grid Points
SIAM Journal on Scientific Computing
A collection of computational techniques for solving singular boundary-value problems
Advances in Engineering Software
Spectral domain embedding for elliptic PDEs in complex domains
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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In this article, a new methodology, Direct Expansion Method of Boundary Condition (DEMBC), is developed to solve 3D elliptic equations in the irregular domain. First, the previous Rational Differential Quadrature Method (Rational Spectral Collocation Method in (Berrut et al. 2005) [8]), developed by Berrut et al. (2005) [8], has been generalized to solve 3D elliptic equations. Second, it is showed that Direct Expansion Method of Boundary Condition is capable of handling boundary problems with higher efficiency. Finally, with the help of conformal mapping (Tee and Trefethen, 2006) [9] and domain decomposition method, DEMBC and 3D-RDQM are able solve three kinds of 3D elliptic equations with small parameters in the irregular domain. Numerous test results justify the accuracy and efficiency of our approach.