Adaptive Method of Particular Solution for Solving 3D Inhomogeneous Elliptic Equations
Recently, particular solutions using radial basis functions have been used as a basis for solving inhomogeneous partial differential equations as a one-stage approach without the need of finding homogeneous solutions. In this paper, we adopt a newly developed adaptive greedy algorithm to enhance the performance of the one-stage method and alleviate the difficulty of ill-conditioning of the resultant matrix. To demonstrate the effectiveness of coupling these two methods, we give two 3D examples with excellent numerical results.
International Journal of Computational Methods
(2010). Adaptive Method of Particular Solution for Solving 3D Inhomogeneous Elliptic Equations. International Journal of Computational Methods, 7(3), 499-511.
Available at: http://aquila.usm.edu/fac_pubs/755