Local Meshless Numerical Method for Solving Transport Problems


Wednesday, 15 October, 2014 - 15:00

Speaker: Gregor Kosec (Parallel And Distributed Systems Laboratory - Jožef Stefan Institute - Ljubljana)

Room: SISSA - Santorio A - room 134

In the last decade, a new class of numerical methods, referred to as the meshless methods, is becoming popular as alternative to classical methods, like Finite Difference Method (FDM), Boundary Element Method (BEM) or Finite Element Method (FEM). A local meshless method (LMM) is based entirely on the approximation constructed over a local subset of scattered computational points and does not require any kind of special topological relations between computational points. The LMM can be formulated in a form suitable for straightforward implementation and further upgrade to treat anomalies such as sharp discontinues or other obscure situations often occurring in complex simulations. Besides simple formulation and implementation, the LMM also enables high parallel efficiency since the localization reduces inter-processor communication, which is often a bottleneck of parallel algorithms. We demonstrate the method on the simulation of (i) natural convection in a free fluid and porous media, (ii) the solidification of a binary alloy, and (iii) the dynamics of charge carrier in a semiconductor device. The basic properties of LMM, i.e. convergence, complexity and intrinsic features, are assessed on the diffusion and Burgers' equations. The parallel efficiency of the presented LMM implementation is demonstrated through the speedup measurements on multicore computer architecture and multi GPU architecture.