Related papers: Integrated photonic multigrid solver for partial d…
Semi-implicit time-stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving…
The Photonic hybRid EleCtromagnetic SolvEr (PRECISE) is a Matlab based library to model large and complex photonics integrated circuits. Each circuit is modularly described in terms of waveguide segments connected through multiport nodes.…
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the…
We introduce a modular approach for efficiently interfacing photonic integrated circuits with deep-sub-wavelength hybrid plasmonic functionality. We demonstrate that an off-the-shelf silicon-on-insulator waveguide can be post-processed into…
The photonic Ising machine is a new paradigm of optical computing that takes advantage of the unique properties of light wave propagation, parallel processing, and low-loss transmission. Thus, the process of solving combinatorial…
Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…
Image processing has become a critical technology in a variety of science and engineering disciplines. While most image processing is performed digitally, optical analog processing has the advantages of being low-power and high-speed though…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…
Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to…
Numerical simulations of quantum chromodynamics (QCD) on a lattice require the frequent solution of linear systems of equations with large, sparse and typically ill-conditioned matrices. Algebraic multigrid methods are meanwhile the…
During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often…
The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses,…
We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
Optical networks with parallel processing capabilities are significant in advancing high-speed data computing and large-scale data processing by providing ultra-width computational bandwidth. In this paper, we present a photonic integrated…
Inverse-designed nanophotonic devices offer promising solutions for analog optical computation. High-density photonic integration is critical for scaling such architectures toward more complex computational tasks and large-scale…