| Space-Time Meshfree Collocation Method for PDEs |
| English |
| Netuzhylov, Hennadiy [> >] |
| Zilian, Andreas  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >] |
| 2009 |
| PAMM |
| WILEY-VCH Verlag |
| 9 |
| 1 |
| 651--652 |
| Yes |
| 1617-7061 |
| [en] An innovative Space-Time Meshfree Collocation Method (STMCM) for solving systems of nonlinear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an alternative to established mesh-based methods. The STMCM belongs to the class of truly meshfree methods, i.e. the methods which do not have any underlying mesh, but work on a set of nodes only, without an a priori node-to-node connectivity. A regularization technique to overcome the singularity-by-construction and to compute all necessary derivatives of the kernel functions is presented. The method combines the simplicity and straightforwardness of the strong-form computational techniques with the advantages of meshfree methods over the classical ones, especially for coupled engineering problems involving moving interfaces. The key features of the proposed approach are: (i) no need to generate a mesh, (ii) simplified imposition of boundary conditions, (iii) no need to evaluate integral forms of governing equations, (iv) applicability to complex irregularly-shaped domains. The proposed STMCM is applied to linear and nonlinear ordinary and partial differential equations of different types and its accuracy and convergence properties are studied. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
| http://hdl.handle.net/10993/11173 |
| 10.1002/pamm.200910295 |
| http://dx.doi.org/10.1002/pamm.200910295 |
