Meshfree collocation method based on interpolating moving least squares

Numerical analysis of transient boundary-coupled multifield problems involving moving, deforming and often topologically changing interfaces is still a difficult issue in computational dynamics. We present a novel Space-Time Meshfree Collocation Method based on Interpolating Moving Least Squares (STMCM-IMLS) and its application to a coupled problem with evolving and deforming interfaces: the problem of biofilm growth. The presented technique is a truly meshfree method in both space and time which provides a straightforward and consistent way of solving partial differential equations. The moving interface is being implicitly tracked solving the level-set equation.