English
Related papers

Related papers: Patch-Smoother and Multigrid for the Dual Formulat…

200 papers

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular…

Numerical Analysis · Mathematics 2016-12-08 Amneet Pal Singh Bhalla , Matthew G. Knepley , Mark F. Adams , Robert D. Guy , Boyce E. Griffith

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

Optimization and Control · Mathematics 2021-06-15 Vladislav Tominin , Yaroslav Tominin , Ekaterina Borodich , Dmitry Kovalev , Alexander Gasnikov , Pavel Dvurechensky

In this article, we propose and study a stochastic and relaxed preconditioned Douglas--Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration…

Optimization and Control · Mathematics 2024-10-01 Yakun Dong , Kristian Bredies , Hongpeng Sun

A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…

Numerical Analysis · Mathematics 2017-03-29 Hehu Xie , Fei Xu

This paper deals with the analysis of a coupled problem arising from linear magneto-elastostaticity. The model, which can be derived by an energy principle, gives valuable insight into the coupling mechanism and features a saddle point…

Analysis of PDEs · Mathematics 2018-02-20 Mané Harutyunyan , Bernd Simeon

This paper considers a recoverable robust single-machine scheduling problem under polyhedral uncertainty with the objective of minimising the total flow time. In this setting, a decision-maker must determine a first-stage schedule subject…

Optimization and Control · Mathematics 2022-03-08 Matthew Bold , Marc Goerigk

We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence…

Analysis of PDEs · Mathematics 2020-07-16 Adriana Garroni , Annalisa Malusa

We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…

Numerical Analysis · Mathematics 2016-10-20 Konstantin Lipnikov , Gianmarco Manzini

Sim-to-real transfer remains a significant challenge in soft robotics due to the unpredictability introduced by common manufacturing processes such as 3D printing and molding. These processes often result in deviations from simulated…

Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional…

Numerical Analysis · Mathematics 2023-02-08 Xiaozhe Hu , Eirik Keilegavlen , Jan M. Nordbotten

This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…

Computational Engineering, Finance, and Science · Computer Science 2024-12-09 Richard Schussnig , Niklas Fehn , Peter Munch , Martin Kronbichler

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…

Optimization and Control · Mathematics 2022-11-01 A. A. Titov , S. S. Ablaev , M. S. Alkousa , F. S. Stonyakin , A. V. Gasnikov

We give sufficient conditions for some underdetermined elliptic PDE of any order to construct smooth compactly supported solutions. In particular we show that two smooth elements in the kernel of certain underdetermined linear elliptic…

Functional Analysis · Mathematics 2011-11-18 Erwann Delay

Based on G. Lan's accelerated gradient sliding and general relation between the smoothness and strong convexity parameters of function under Legendre transformation we show that under rather general conditions the best known bounds for…

Optimization and Control · Mathematics 2020-01-03 Mohammad Alkousa , Darina Dvinskikh , Fedor Stonyakin , Alexander Gasnikov , Dmitry Kovalev

We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…

Machine Learning · Computer Science 2023-09-29 Jérôme Bolte , Edouard Pauwels , Antonio Silveti-Falls

We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…

Numerical Analysis · Mathematics 2018-09-07 Martin Čermák , Stanislav Sysala , Jan Valdman

We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming…

Numerical Analysis · Mathematics 2017-05-22 Shuonan Wu , Shihua Gong , Jinchao Xu

Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…

Numerical Analysis · Mathematics 2019-07-24 Peter Bastian , Eike Hermann Müller , Steffen Müthing , Marian Piatkowski

Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…

Computational Physics · Physics 2020-10-13 Jiamin Jiang , Xian-Huan Wen

In this work, we propose a mixed finite element method for solving elliptic multiscale problems based on a localized orthogonal decomposition (LOD) of Raviart-Thomas finite element spaces. It requires to solve local problems in small…

Numerical Analysis · Mathematics 2016-06-21 Fredrik Hellman , Patrick Henning , Axel Målqvist