Polynomial Particular Solutions For Poisson Problems
Free (open access)
A S Muleshkov, M A Golberg, A H-D Cheng & C S Chen
High dimensional Chebyshev interpolation scheme was used to approximate the right hand side of Poisson's equation. Symbolic software such as Mathematica is essential for the expansion of Chebyshev polynomial. Particular solution of monomial was employed repeatly to the approximate Chebyshev polynomial and the particular solution of overall Poisson' equation can be obtained. The method of fundamental solutions was used to solve the homogeneous equation. One of the major advantages of such approach is that no matrix inversion is required. The solution procedure can be extended and implemented from 2D to 3D problems easily. To illustrate the effectiveness of the proposed approach, the numerical solution of a 2D Poisson problem is given.