相关论文: Accurate Coarse Residual for Two-Level Asynchronou…

In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…

We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…

We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…

This paper seeks to combine dictionary learning and hierarchical image representation in a principled way. To make dictionary atoms capturing additional information from extended receptive fields and attain improved descriptive capacity, we…

We give a novel convergence theory for two-level hybrid Schwarz domain-decomposition (DD) methods for finite-element discretisations of the high-frequency Helmholtz equation. This theory gives sufficient conditions for the preconditioned…

We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz…

We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to…

Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…

This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…

Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirable feature to have in a numerical formulation for multiscale…

Off-the-shelf pre-trained Automatic Speech Recognition (ASR) systems are an increasingly viable service for companies of any size building speech-based products. While these ASR systems are trained on large amounts of data, domain mismatch…

We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…

Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…

Asynchronous iterations are more and more investigated for both scaling and fault-resilience purpose on high performance computing platforms. While so far, they have been exclusively applied within space domain decomposition frameworks,…

In this paper, we propose an overlapping additive Schwarz method for total variation minimization based on a dual formulation. The $O(1/n)$-energy convergence of the proposed method is proven, where $n$ is the number of iterations. In…

The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a…

Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…

Local decoders, also known as cellular-automaton decoders, offer a promising path toward real-time quantum error correction by replacing centralized classical decoding, with inherent hardware constraints, by a natively parallel and…

We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…

In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…