Stuart R. Slattery

Mesh-free data transfer algorithms for partitioned multiphysics problems

In this paper we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. These scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

Summary We consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. These methods are expected to have considerable potential for resiliency to faults when implemented on massively parallel machines. We establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Local Improvement Results for Anderson Acceleration with Inaccurate Function Evaluations

We analyze the convergence of Anderson acceleration when the fixed point map is corrupted with errors. We consider uniformly bounded errors and stochastic errors with infinite tails. We prove local improvement results which describe the performance of the iteration up to the point where the accuracy of the function evaluation causes the iteration to stagnate. We illustrate the results with examples from neutronics.

DTK C/Fortran Interface Development for NEAMS FSI Simulations

This report documents the development of DataTransferKit (DTK) [19] C and Fortran interfaces for fluid-structure-interaction (FSI) simulations in NEAMS. In these simulations, the codes Nek5000 [8] and Diablo [13] are being coupled within the SHARP [17] framework to study flow-induced vibration (FIV) in reactor steam generators [12]. We will review the current Nek5000/Diablo coupling algorithm in SHARP and the current state of the solution transfer scheme used in this implementation. We will then present existing DTK algorithms which may be used instead to provide an improvement in both flexibility and scalability of the current SHARP implementation. We will show how these can be used within the current FSI scheme using a new set of interfaces to the algorithms developed by this work. These new interfaces currently expose the mesh-free solution transfer algorithms in DTK, a C++ library, and are written in C and Fortran to enable coupling of both Nek5000 and Diablo in their native Fortran language. They have been compiled and tested on Cooley, the test-bed machine for Mira at ALCF.