Related papers: Integrated photonic multigrid solver for partial d…
A hybrid Schwarz/multigrid method for spectral element solvers to the Poisson equation in $\mathbb R^2$ is presented. It extends the additive Schwarz method studied by J. Lottes and P. Fischer (J. Sci. Comput. 24:45--78, 2005) by…
Advanced artificial intelligence (AI) algorithms, particularly those based on artificial neural networks, have garnered significant attention for their potential applications in areas such as image recognition and natural language…
We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…
NP-complete problems are widely and deeply involved in various real-life scenarios while still intractable to solve efficiently on conventional computers. It is of great practical significance to construct versatile computing architectures…
Recent advancements in quantum photonics have driven significant progress in photonic quantum computing (PQC), addressing challenges in scalability, efficiency, and fault tolerance. Experimental efforts have focused on integrated photonic…
Many developments in science and engineering depend on tackling complex optimizations on large scales. The challenge motivates intense search for specific computing hardware that takes advantage from quantum features, nonlinear dynamics, or…
In the present work, we study how to develop an efficient solver for the fast resolution of large and sparse linear systems that occur while discretizing elliptic partial differential equations using isogeometric analysis. Our new approach…
Optical computing often employs tailor-made hardware to implement specific algorithms, trading generality for improved performance in key aspects like speed and power efficiency. An important computing approach that is still missing its…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
Photonics has been one of the primary beneficiaries of advanced silicon manufacturing. By leveraging on mature complementary metal-oxide-semiconductor (CMOS) process nodes, unprecedented device uniformities and scalability have been…
Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…
Scalable photonic quantum computing architectures pose stringent requirements on photonic processing devices. The need for low-loss high-speed reconfigurable circuits and near-deterministic resource state generators are some of the most…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
Designing modern photonic devices often involves traversing a large parameter space via an optimization procedure, gradient based or otherwise, and typically results in the designer performing electromagnetic simulations of correlated…
The slowing down of Moore's law has driven the development of application-specific processors for deep learning. Analog photonic processors offer a promising solution for accelerating matrix-vector multiplications (MVMs) in deep learning by…
We propose a universal approach for modeling complex integrated photonic resonators based on the scattering matrix method. By dividing devices into basic elements including directional cou-plers and connecting waveguides, our approach can…
In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which…
Integrated photonic devices have become pivotal elements across most research fields that involve light-based applications. A particularly versatile category of this technology are programmable photonic integrated processors, which are…
Neural networks find widespread use in scientific and technological applications, yet their implementations in conventional computers have encountered bottlenecks due to ever-expanding computational needs. Photonic neuromorphic hardware,…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…