A domain decomposition python framework with autosaving of subdomain solutions for finite element analysis

Abstract

Domain decomposition methods in Finite Elements (FE) can be summarized as dividing the boundary value problem into smaller boundary value problems in subdomains and using the realized subdomain solutions to coordinate a general solution of the given system domain. Domain decomposition methods are appropriate for parallel computing since the problem on a prescribed subdomain can be partially solved independent of the whole system domain, thus, those individual solutions can be implemented on different CPUs and subsequently combined. The independence aspect of the subdomain solutions not only enables parallel programming but also allows for the efficient storage and reuse of the already realized subdomain solutions in other systems. Thus, it is possible to implement existing subdomain solutions instead of having to completely rework the problem in the event of minor changes to a few components of the system, potentially saving significant calculation time. In this thesis, a domain decomposition framework interface is proposed that, by adding a few straightforward definitions to the end-user code, will automatically enhance a traditional FE application written in Python to support domain decomposition with self-registering and reusable subdomains. To register and reuse a subdomain solution, it is necessary to create a hash string that uniquely represents the corresponding subdomain. This includes traversing all the properties of all individual items that make up the subdomain, such as all element and node properties and all boundary conditions. Special Python decorators that enable the end user to introduce variables of the functions in the end user code to the decomposition framework have been developed to streamline the process. In addition, standard components that automatically decompose end-user-defined FE objects into subdomains are also presented within the scope of the thesis. As a result, using various sample solid mechanics applications, the contribution of the proposed framework to the analysis speed is evaluated.