Related papers: A parallel directional Fast Multipole Method
We consider the use of multipreconditioning, which allows for multiple preconditioners to be applied in parallel, on high-frequency Helmholtz problems. Typical applications present challenging sparse linear systems which are complex…
Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…
Due to the variety and importance of applications of treecodes and FMM, the combination of algorithmic acceleration with hardware acceleration can have tremendous impact. Alas, programming these algorithms efficiently is no piece of cake.…
Kernel matrices appear in machine learning and non-parametric statistics. Given $N$ points in $d$ dimensions and a kernel function that requires $\mathcal{O}(d)$ work to evaluate, we present an $\mathcal{O}(dN\log N)$-work algorithm for the…
The problem of identifying intersections between two sets of d-dimensional axis-parallel rectangles appears frequently in the context of agent-based simulation studies. For this reason, the High Level Architecture (HLA) specification -- a…
Particle filter (PF) sequential Monte Carlo (SMC) methods are very attractive for the estimation of parameters of time dependent systems where the data is either not all available at once, or the range of time constants is wide enough to…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
We propose an overlapping Schwarz space-time refinement framework for the material point method (OS-MPM) to improve computational efficiency in problems with strongly localized deformation, contact, and large geometric nonlinearity. The…
We present a new scheme to compensate for the small-scales approximations resulting from Particle-Mesh (PM) schemes for cosmological N-body simulations. This kind of simulations are fast and low computational cost realizations of the large…
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…
Multiple kernel learning (MKL) aims to find an optimal, consistent kernel function. In the hierarchical multiple kernel clustering (HMKC) algorithm, sample features are extracted layer by layer from a high-dimensional space to maximize the…
We present a hybrid OpenMP/Charm++ framework for solving the $\mathcal{O} (N)$ Self-Consistent-Field eigenvalue problem with parallelism in the strong scaling regime, $P\gg{N}$, where $P$ is the number of cores, and $N$ a measure of system…
We introduce a high-performance virtual machine (VM) written in a numerically fast language like Fortran or C to evaluate very large expressions. We discuss the general concept of how to perform computations in terms of a VM and present…
The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the…
Optical kernel machines offer high throughput and low latency. A nonlinear optical kernel can handle complex nonlinear data, but power consumption is typically high with the conventional nonlinear optical approach. To overcome this issue,…
The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the fast Fourier transform (FFT), the fast multipole method (FMM), the geometric multigrid (GMG), and…
Collaboratively fine-tuning (FT) large language models (LLMs) over heterogeneous mobile devices fosters immense potential applications of personalized intelligence. However, such a vision faces critical system challenges. Conventional…