Sparse matrix computations, in the form of solvers for systems of linear equations, eigenvalue problem or matrix factorizations constitute the main kernel in problems from fields as diverse as computational fluid dynamics, quantum many body problems, machine learning and graph analytics. Iterative eigensolvers have been preferred over the regular method because the regular method not being feasible with industrial sized matrices. Although dense linear algebra libraries like BLAS, LAPACK, SCALAPACK are well established and some vendor optimized implementation like mkl from Intel or Cray Libsci exist, it is not the same case for sparse linear algebra which is lagging far behind. The main reason behind slow progress in the standardization of sparse linear algebra or library development is the different forms and properties depending on the application area. It is worsened for deep memory hierarchies of modern architectures due to low arithmetic intensities and memory bound computations. Minimization of data movement and fast access to the matrix are critical in this case. Since the current technology is driven by deep memory architectures where we get the increased capacity at the expense of increased latency and decreased bandwidth when we go further from the processors. The key to achieve high performance in sparse matrix computations in deep memory hierarchy is to minimize data movement across layers of the memory and overlap data movement with computations. My thesis work contributes towards addressing the algorithmic challenges and developing a computational infrastructure to achieve high performance in scientific applications for both shared memory and distributed memory architectures. For this purpose, I started working on optimizing a blocked eigensolver and optimized specific computational kernels which uses a new storage format. Using this optimization as a building block, we introduce a shared memory task parallel framework focusing on optimizing the entire solvers rather than a specific kernel. Before extending this shared memory implementation to a distributed memory architecture, I simulated the communication pattern and overheads of a large scale distributed memory application and then I introduce the communication tasks in the framework to overlap communication and computation. Additionally, I also tried to find a custom scheduler for the tasks using a graph partitioner. To get acquainted with high performance computing and parallel libraries, I started my PhD journey with optimizing a DFT code named Sky3D where I used dense matrix libraries. Despite there might not be any single solution for this problem, I tried to find an optimized solution. Though the large distributed memory application MFDn is kind of the driver project of the thesis, but the framework we developed is not confined to MFDn only, rather it can be used for other scientific applications too. The output of this thesis is the task parallel HPC infrastructure that we envisioned for both shared and distributed memory architectures.
Read
