A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices

We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of Approximate Computing, allowing imprecision in the final result in order to be able to utilize the sparsity of the input matrix and to allow massively parallel execution. For an n x n matrix, the proposed algorithm allows to distribute the calculations over n nodes with only little communication overhead. The approximate result matrix exhibits the same sparsity pattern as the input matrix, allowing for efficient reuse of allocated data structures. We evaluate the algorithm with respect to the error that it introduces into calculated results, as well as its performance and scalability. We demonstrate that the error is relatively limited for well-conditioned matrices and that results are still valuable for error-resilient applications like preconditioning even for ill-conditioned matrices. We discuss the execution time and scaling of the algorithm on a theoretical level and present a distributed implementation of the algorithm using MPI and OpenMP. We demonstrate the scalability of this implementation by running it on a high-performance compute cluster comprised of 1024 CPU cores, showing a speedup of 665x compared to single-threaded execution

Computational linear algebra over finite fields

We present here algorithms for efficient computation of linear algebra problems over finite fields

Automated Code Generation for Lattice Quantum Chromodynamics and beyond

We present here our ongoing work on a Domain Specific Language which aims to simplify Monte-Carlo simulations and measurements in the domain of Lattice Quantum Chromodynamics. The tool-chain, called Qiral, is used to produce high-performance OpenMP C code from LaTeX sources. We discuss conceptual issues and details of implementation and optimization. The comparison of the performance of the generated code to the well-established simulation software is also made