Related papers: Breaking Boundaries: Distributed Domain Decomposit…
The simulation of three dimensional magnetostatic problems plays an important role, for example when simulating synchronous electric machines. Building on prior work that developed a domain decomposition algorithm using isogeometric…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $\rho$, which is the fundamental description for…
The decode-forward achievable region is studied for general networks. The region is subject to a fundamental tension in which nodes individually benefit at the expense of others. The complexity of the region depends on all the ways of…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
A new flow solver scalable on multiple Graphics Processing Units (GPUs) for direct numerical simulation of wall-bounded incompressible flow is presented. This solver utilizes a previously reported work (J. Comp. Physics, vol. 352 (2018),…
We extend the Balancing Domain Decomposition by Constraints (BDDC) method to flows in porous media discretised by mixed-hybrid finite elements with combined mesh dimensions. Such discretisations appear when major geological fractures are…
Modelling forced dynamical systems - where an external input drives the system state - is critical across diverse domains such as engineering, finance, and the natural sciences. In this work, we propose Laplace-Net, a decoupled, solver-free…
We address in this thesis the current need to design new parallel algorithms and tools that ease the development of geodynamic modelling applications that are suited for today's and tomorrow's hardware. We present (1) the MATLAB HPC…
We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
Simulations of physical phenomena are essential to the expedient design of precision components in aerospace and other high-tech industries. These phenomena are often described by mathematical models involving partial differential equations…
In recent years inpainting-based compression methods have been shown to be a viable alternative to classical codecs such as JPEG and JPEG2000. Unlike transform-based codecs, which store coefficients in the transform domain, inpainting-based…
We consider the distributed training of large-scale neural networks that serve as PDE solvers producing full field outputs. We specifically consider neural solvers for the generalized 3D Poisson equation over megavoxel domains. A scalable…
Progress in machine learning (ML) has been fueled by scaling neural network models. This scaling has been enabled by ever more heroic feats of engineering, necessary for accommodating ML approaches that require high bandwidth communication…
While 3D Gaussian Splatting (3DGS) excels in static scene modeling, its extension to dynamic scenes introduces significant challenges. Existing dynamic 3DGS methods suffer from either over-smoothing due to low-rank decomposition or feature…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
Inference scaling methods for LLMs often rely on decomposing problems into steps (or groups of tokens), followed by sampling and selecting the best next steps. However, these steps and their sizes are often predetermined or manually…
Starting from the single graphics processing unit (GPU) version of the Smoothed Particle Hydrodynamics (SPH) code DualSPHysics, a multi-GPU SPH program is developed for free-surface flows. The approach is based on a spatial decomposition…