Predavanje: dr. sc. Gregor Kosec – “Implementation of strong form meshfree methods for solving PDEs”

04. studenog 2019.

od 12:15  do –

A219, FESB

Sažetak predavanja:

Since the first appearance of Meshfree method for solving partial differential equations (PDEs) back in the seventies, many strong and weak form Meshfree methods emerged, mostly generalizing the mesh based strong form Finite Difference Method (FDM) and mesh based weak form Finite Element Method (FEM). While mesh based methods are well supported with a number of high quality software implementations, e.g. deal.II, FEniCS, FreeFem++, etc., in the Meshfree community such implementations are rare. The most notable open source Meshfree project is the DualSPHysics, which is fully focused on SPH. There are also projects offering Matlab scripts and domain specific applications, such as MFDMtool, GEC_RBFFD, MFree2D, as well as a Python package containing tools for radial basis function. Here, we present a C++ implementation of a tool set that can be used to construct several reported strong form Meshfree methods, such as Diffuse Approximate Method (DAM), Radial Basis Function-generated Finite Differences (RBF-FD), Generalized FDM, Collocated discrete least squares (CDLS) and many more. In the presented C++ implementation different Meshfree methods are constructed by combining appropriate modules in a desired final solution procedure. Many Meshfree methods, such as RBF-FD, do not depend on the dimension of the considered domain. In the presented implementation this is inherently translated into the code, as all modules are templated with respect to domain dimension, which results in dimension independent code. Special care is also taken to increase expressiveness of the code to facilitate the translation of mathematical notation of the considered problem into the source code. We will discuss main modules of meshless procedure, theirs implementation and demonstration of the solution procedure on different cases ranging from simple solution of Poisson equation in 2D to the coupled non-linear system of PDEs describing thermo-fluid dynamics in irregular 3D domain.

Prilog:

• cv