A space-time meshfree collocation method for coupled problems

An innovative Space-Time Meshfree Collocation Method (STMCM) for solving systems of 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. The goal is to design a method that 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.