Research Projects

The goal of this project is to develop fast numerical linear algebra libraries that are scalable on massively parallel heterogeneous architecture. The class of numerical linear algebra problems that we will be focusing on are those arising out of large N-body problems such as integral equations from modelling of physical phenomena (such as wave propagation, diffusion, etc.), particle simulations, radial basis function interpolation, geo-statistics, support vector machines, kernel density estimation, Gaussian process regression, etc. Given the wide applicability of large scale N-body problems, it is imperative to possess fast computational algorithms that can leverage massively parallel heterogeneous architecture. Fast computational algorithms on massively parallel heterogeneous architecture are required to solve such large N-body problems. The class of algorithms that we will be looking at are those that (i) grow linearly or almost linearly in the underlying degrees of freedom N; (ii) are designed for parallel architectures. The matrices that result from N-body problems have a hierarchical low-rank structure. Many fast algorithms for N-body problems, including the Fast Multipole Method (FMM) and hierarchical matrix algorithms, have been built on this foundation (FMM can also be considered a subclass of hierarchical matrix algorithms). The construction of hierarchical matrices is based on the idea that some sub-matrices of the matrix corresponding to N-body problems can be efficiently approximated by low-rank matrices. By utilising cutting-edge computing resources, the hierarchical matrix techniques for N-body problems can be significantly accelerated. Depending on the available architecture, there are numerous possibilities for parallelising an algorithm. An example would be using a GPU or distributed/shared memory system. Codes created for one type of architecture cannot be used with another. Hence, there is a need to have a single unified parallel code for fast algorithms developed for a heterogeneous architecture so that the implementation of the algorithms is not a hindrance to applying them in real-life applications. Our areas of focus include developing a parallel implementation of the hierarchical matrix algorithms using OpenACC, minimising communication costs, balancing workload across several processor units, optimising cache usage, etc. To the best of our knowledge, there exists no generic parallel implementation of the H-matrix algorithms for heterogeneous architectures. Therefore this project will pave way for a new direction of research in high performance computing for H matrices. Further, there is no existing hard rule to choose the H-matrix that performs better on a given architecture. This project will enable end-users applying these algorithms to choose the right H-matrix algorithm for the given problem and computing architecture.