An effective Chebyshev tau meshless domain decomposition method based on the integration–differentiation for solving fourth order equations

In this paper, we present a method, which combines the Chebyshev tau meshless method based on the integration–differentiation (CTMMID) with Domain Decomposition Method (DDM), and apply it to solve the fourth order problem on irregular domains. This method, i.e. CTMMID-DDM, is an improvement of our previous job. In early work, it shows that the CTMMID can solve the fourth order problems well in square domain, and leads to the condition number which grows like O(N4)O(N4), but it becomes worse when we apply it on irregular domains directly. DDMs extend the applicability of spectral methods to handle complex geometries and large-scale problems. Numerical results show that CTMMID-DDM works well, it circumvents the ill-conditioning problem, further attains a improvement in solution accuracy, and also makes us feasible to solve the problems with boundary layers.