Abstract: In this work we present the novel numerical method solving multicomponent Smoluchowski coagulation equation. The new method is based on application of the fast algorithms of linear algebra and the fast arithmetics in tensor train format to acceleration of well-known highly accurate second order Runge-Kutta scheme. After the application of proposed algorithmic optimizations we obtain a dramatical speedup of the classical methodology without loss of the accuracy. We test our solver the problem with source and sink terms and obtain that the TT-ranks of numerical solution do not grow tremendously even with the insert of the physical effects into the basic Smolushowski coagulation model.

Abstract: Various optimization algorithms have been proposed to compute the Karcher mean (namely the Riemannian center of mass in the sense of the affine-invariant metric) of a collection of symmetric positive-definite matrices. Here we propose to handle this computational task with a recently developed limited-memory Riemannian BFGS method using an implementation tailored to the symmetric positive-definite Karcher mean problem. We also demonstrate empirically that the method is best suited for large-scale problems in terms of computation time and robustness when comparing to the existing state-of-the-art algorithms.

Abstract: The Gravitational Wave (GW) detectors, advanced LIGO and advanced Virgo, are acquiring the potential for recording unprecedented astronomic data for astrophysical events. The Mario Schenberg detector (MSD) is a smaller scale experiment that could participate to this search. Previously, we developed a first data analysis pipeline (DAP) to transform the detector's signal into relevant GW information. This pipeline was extremely simplified in order to be executed in low-latency. In order to improve the analysis methods while keeping a low execution time, we propose three different parallel approaches using GPU/CUDA. We implemented the parallel models using cuBLAS library functions and enhance its capability with asynchronous processes in CUDA streams. Our novel model achieves performances that surpass the serial implementation within the data analysis pipeline by a speed up of 21% faster than the traditional model. This first result is part of a more comprehensive approach, in which all DAP modules that can be parallelized, are being re-written in GPGP/CUDA, and then tested and validated within the MSD context.