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The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a…

Robotics · Computer Science 2018-09-20 Liang Zhao , Shoudong Huang , Gamini Dissanayake

We introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level…

Numerical Analysis · Mathematics 2025-09-26 Youngkyu Lee , Alena Kopaničáková , George Em Karniadakis

This paper introduces a robust preconditioner for general sparse symmetric matrices, that is based on low-rank approximations of the Schur complement in a Domain Decomposition (DD) framework. In this "Schur Low Rank" (SLR) preconditioning…

Numerical Analysis · Computer Science 2015-05-19 Ruipeng Li , Yuanzhe Xi , Yousef Saad

In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global…

Numerical Analysis · Mathematics 2019-10-21 Gabriele Ciaramella , Muhammad Hassan , Benjamin Stamm

Incompressible fluid flow problems appear frequently in different applications. The discretization of such problems may result in large and ill-conditioned systems of linear equations. We consider the case of the Stokes equations…

Numerical Analysis · Mathematics 2025-12-02 Filipe Cumaru , Alexander Heinlein , Joachim Schöberl

A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the…

Numerical Analysis · Mathematics 2012-04-10 Jing Li , Xuemin Tu

Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…

Numerical Analysis · Mathematics 2019-10-09 Jehanzeb Chaudhry , Don Estep , Simon Tavener

We study the convergence properties of an overlapping Schwarz decomposition algorithm for solving nonlinear optimal control problems (OCPs). The algorithm decomposes the time domain into a set of overlapping subdomains, and solves all…

Optimization and Control · Mathematics 2026-05-11 Sen Na , Sungho Shin , Mihai Anitescu , Victor M. Zavala

The Helmholtz equation poses significant computational challenges due to its oscillatory solutions, particularly for large wavenumbers. Inspired by the Schur complement system for elliptic problems, this paper presents a novel…

Numerical Analysis · Mathematics 2025-05-02 Yi Yu , Marcus Sarkis , Guanglian Li , Zhiwen Zhang

We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The…

Numerical Analysis · Mathematics 2024-04-03 Jeffrey Galkowski , Shihua Gong , Ivan G. Graham , David Lafontaine , Euan A. Spence

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…

Numerical Analysis · Mathematics 2020-03-23 Marcella Bonazzoli , Victorita Dolean , Ivan G. Graham , Euan A. Spence , Pierre-Henri Tournier

Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of…

Numerical Analysis · Mathematics 2025-06-23 Boris Martin , Pierre Jolivet , Christophe Geuzaine

We present a two-level overlapping Schwarz preconditioner for three-dimensional problems discretized with the Virtual Element Method. Our approach handles general polyhedral meshes and irregular subdomains, extending the applicability of…

Numerical Analysis · Mathematics 2025-12-09 Ana Aguilar-Pineda , Luis F. Amey , Adrian Angulo-Paniagua , Juan G. Calvo

Two-level domain decomposition preconditioners lead to fast convergence and scalability of iterative solvers. However, for highly heterogeneous problems, where the coefficient function is varying rapidly on several possibly non-separated…

Numerical Analysis · Mathematics 2022-07-13 Alexander Heinlein , Kathrin Smetana

In this paper, we propose a two-level overlapping additive Schwarz domain decomposition preconditioner for the symmetric interior penalty discontinuous Galerkin method for the second order elliptic boundary value problem with highly…

Numerical Analysis · Mathematics 2018-10-16 Erik Eikeland , Leszek Marcinkowski , Talal Rahman

An efficient strategy to construct physics-based local surrogate models for parametric linear elliptic problems is presented. The method relies on proper generalized decomposition (PGD) to reduce the dimensionality of the problem and on an…

Numerical Analysis · Mathematics 2025-12-03 Marco Discacciati , Ben J. Evans , Matteo Giacomini

We propose two variants of the overlapping additive Schwarz method for the finite element discretiza- tion of the elliptic problem in 3D with highly heterogeneous coefficients. The methods are efficient and simple to construct using the…

Numerical Analysis · Mathematics 2016-11-04 Erik Eikeland , Leszek Marcinkowski , Talal Rahman

Optimizing robot poses and the map simultaneously has been shown to provide more accurate SLAM results. However, for non-feature based SLAM approaches, directly optimizing all the robot poses and the whole map will greatly increase the…

Robotics · Computer Science 2025-01-23 Yingyu Wang , Liang Zhao , Shoudong Huang

In this paper, we study the back-end of simultaneous localization and mapping (SLAM) problem in deforming environment, where robot localizes itself and tracks multiple non-rigid soft surface using its onboard sensor measurements. An…

Robotics · Computer Science 2019-06-21 Jingwei Song , Liang Zhao , Shoudong Huang , Gamini Dissanayake

In the current work we present a spectral analysis of the additive and multiplicative Schwarz methods within the framework of domain decomposition techniques, by investigating the spectral properties of these classical Schwarz…

Numerical Analysis · Mathematics 2026-02-05 Abdessadek Rifqui , Ahmed Ratnani , Stefano Serra-Capizzano