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Astrophysical research in recent decades has made significant progress thanks to the availability of various $N$-body simulation techniques. With the rapid development of high-performance computing technologies, modern simulations have been…
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to a…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…
The development of multicore architectures supporting parallel data processing has led to a paradigm shift, which affects communication systems significantly. This article provides a scalable parallel approach of an iterative LDPC decoder,…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
The goal of this work is to parallelize the multistep scheme for the numerical approximation of the backward stochastic differential equations (BSDEs) in order to achieve both, a high accuracy and a reduction of the computation time as…
Ab initio Born-Oppenheimer molecular dynamics (AIMD) is a valuable method for simulating physico-chemical processes of complex systems, including reactive systems, and for training machine learning models and force fields. Speed and…
We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…
An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent…
Due to the very rapidly growing use of Artificial Neural Networks (ANNs) in real-world applications related to machine learning and Artificial Intelligence (AI), several hardware accelerator de-signs for ANNs have been proposed recently. In…
The growing demand for deploying Small Language Models (SLMs) on edge devices, including laptops, smartphones, and embedded platforms, has exposed fundamental inefficiencies in existing accelerators. While GPUs handle prefill workloads…
This paper applies the N-block PCPM algorithm to solve multi-scale multi-stage stochastic programs, with the application to electricity capacity expansion models. Numerical results show that the proposed simplified N-block PCPM algorithm,…
Phase clocks are synchronization tools that implement a form of logical time in distributed systems. For systems tolerating transient faults by self-repair of damaged data, phase clocks can enable reasoning about the progress of distributed…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU…
Detailed chemistry-based computational fluid dynamics (CFD) simulations are computationally expensive due to the solution of the underlying chemical kinetics system of ordinary differential equations (ODEs). Here, we introduce a novel…
Current soft processor architectures for FPGAs do not utilize the potential of the massive parallelism available. FPGAs now support many thousands of embedded floating point operators, and have similar computational densities to GPGPUs.…
Graphic Processing Units (GPUs) are getting increasingly important as target architectures in scientific High Performance Computing (HPC). NVIDIA established CUDA as a parallel computing architecture controlling and making use of the…
Probabilistic breadth-first traversals (BPTs) are used in many network science and graph machine learning applications. In this paper, we are motivated by the application of BPTs in stochastic diffusion-based graph problems such as…
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…