Parallelization of least square meshfree methods: Data management and domain decomposition solvers
Tiwari, Mayank Manjul
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In recent years, meshfree methodology has been developed as an alternative to the traditional mesh based methods and has been used to solve problems like crack propagation and large deformation. Among the several formulations used is the Least Square based meshfree method which circumvents volumetric locking, is robust to integration errors and results in a symmetric positive definite system. Despite these advantages, the complexity of meshfree shape functions along with their arbitrary location and support makes them computationally more expensive when compared to standard finite elements. In this work, a parallel adaptive implementation of the Least square meshfree method is presented. It has been implemented on the Adaptive Finite Elements Application Programmers Interface (AFEAPI) framework. Standard iterative solvers have been implemented along with domain decomposition based preconditioners resulting in a significant decrease in overall computation time and the ability to do large scale systems. The methodology has been tested by solving the Stokes problem and a problem arising from a simple continuum plasticity model of granular flow. Both problems are solved in a distributed memory multi-processor environment.