相关论文: GPU Optimizations for the Hierarchical Poincar\'e-…

We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz…

We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an interplay between domain decomposition methods and HDG…

We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…

This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Fully Homomorphic Encryption (FHE) enables secure computation over encrypted data, but its computational cost remains a major obstacle to practical deployment. To mitigate this overhead, many studies have explored GPU acceleration for the…

In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm,…

Hyperdimensional computing (HD) is an emerging paradigm for machine learning based on the evidence that the brain computes on high-dimensional, distributed, representations of data. The main operation of HD is encoding, which transfers the…

We present a highly general implementation of fast multipole methods on graphics processing units (GPUs). Our two-dimensional double precision code features an asymmetric type of adaptive space discretization leading to a particularly…

In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…

Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…

In this paper, we propose a new set of midpoint-based high-order discretization schemes for computing straight and mixed nonlinear second derivative terms that appear in the compressible Navier-Stokes equations. Firstly, we detail a set of…

The boundary layer represents a fundamental structure in fluid dynamics, where accurate boundary discretization significantly enhances computational efficiency. This paper presents a third-order boundary discretization for compact…

We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs). The method transforms the IHOCs into finite-horizon optimal…

The calculation of g-functions is essential for the design and simulation of geothermal boreholes. However, existing methods, such as the stacked finite line source (SFLS) model, face challenges regarding computational efficiency and…

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to…

In the era of big data, methods for improving memory and computational efficiency have become crucial for successful deployment of technologies. Hashing is one of the most effective approaches to deal with computational limitations that…

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…

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…

We analyze a novel multi-level version of a recently introduced compressed sensing (CS) Petrov-Galerkin (PG) method from [H. Rauhut and Ch. Schwab: Compressive Sensing Petrov-Galerkin approximation of high-dimensional parametric operator…