Publications

In scientific computing, the acceleration of atomistic computer simulations by means of custom hardware is finding ever-growing application. A major limitation, however, is that the high efficiency in terms of performance and low power consumption entails the massive usage of low precision computing units. Here, based on the approximate computing paradigm, we present an algorithmic method to compensate for numerical inaccuracies due to low accuracy arithmetic operations rigorously, yet still obtaining exact expectation values using a properly modified Langevin-type equation.

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-theart ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

We address the general mathematical problem of computing the inverse p-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary p-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter q always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various matrices with different densities, condition numbers and spectral radii.

Approximate computing has shown to provide new ways to improve performance and power consumption of error-resilient applications. While many of these applications can be found in image processing, data classification or machine learning, we demonstrate its suitability to a problem from scientific computing. Utilizing the self-correcting behavior of iterative algorithms, we show that approximate computing can be applied to the calculation of inverse matrix p-th roots which are required in many applications in scientific computing. Results show great opportunities to reduce the computational effort and bandwidth required for the execution of the discussed algorithm, especially when targeting special accelerator hardware.

Branch and bound (B&B) algorithms structure the search space as a tree and eliminate infeasible solutions early by pruning subtrees that cannot lead to a valid or optimal solution. Custom hardware designs significantly accelerate the execution of these algorithms. In this article, we demonstrate a high-performance B&B implementation on FPGAs. First, we identify general elements of B&B algorithms and describe their implementation as a finite state machine. Then, we introduce workers that autonomously cooperate using work stealing to allow parallel execution and full utilization of the target FPGA. Finally, we explore advantages of instance-specific designs that target a specific problem instance to improve performance. We evaluate our concepts by applying them to a branch and bound problem, the reconstruction of corrupted AES keys obtained from cold-boot attacks. The evaluation shows that our work stealing approach is scalable with the available resources and provides speedups proportional to the number of workers. Instance-specific designs allow us to achieve an overall speedup of 47 × compared to the fastest implementation of AES key reconstruction so far. Finally, we demonstrate how instance-specific designs can be generated just-in-time such that the provided speedups outweigh the additional time required for design synthesis.