Abstract
Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson's equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomogeneous term, while the homogeneous solution is obtained by linear combination of a set of T-Trefftz solutions. The present scheme, named RBF-Trefftz has the advantage over the fundamental solution (MFS) method due to the use of nonsingular T-Trefftz solution rather than singular fundamental solutions, so it does not require the artificial boundary. The application and efficiency of the proposed method are validated through several examples which include different type of differential equations, such as Laplace equation, Hellmholtz equation, convectin-diffusion equation and time-dependent equation.
| Original language | English |
|---|---|
| Article number | 012217 |
| Journal | IOP Conference Series: Materials Science and Engineering |
| Volume | 10 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2014 |
| Event | 9th World Congress on Computational Mechanics, WCCM 2010, Held in Conjuction with the 4th Asian Pacific Congress on Computational Mechanics, APCOM 2010 - Sydney, Australia Duration: 19 Jul 2010 → 23 Jul 2010 |