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Related papers: Hybridised multigrid preconditioners for a compati…

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This paper mainly considers three iterations based on charge-conservative finite element approximation in Lipschitz domain for the stationary thermally coupled inductionless MHD equations. Based on the hybrid finite element method, the…

Analysis of PDEs · Mathematics 2023-03-22 Shitian Dong , Haiyan Su

In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…

Numerical Analysis · Mathematics 2017-04-26 Shihua Gong , Shuonan Wu , Jinchao Xu

The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-06-16 Eike H. Mueller , Robert Scheichl

We propose parameter-robust preconditioners for the statically condensed linear system arising from a hybridizable discontinuous Galerkin discretization of the coupled Stokes--Darcy system. The design strategy relies on first applying the…

Numerical Analysis · Mathematics 2026-04-27 Esteban Henríquez , Miroslav Kuchta , Jeonghun J. Lee , Sander Rhebergen

This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…

Numerical Analysis · Mathematics 2020-11-30 Lukas Kogler , Joachim Schöberl

A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…

Numerical Analysis · Mathematics 2018-01-08 Yuliya Gorb , Daria Kurzanova , Yuri Kuznetsov

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic…

Numerical Analysis · Mathematics 2019-03-28 P. F. Antonietti , P. Houston , G. Pennesi , E. Süli

In this work we construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a…

Numerical Analysis · Mathematics 2012-07-13 Andrei Draganescu , Ana Maria Soane

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…

Numerical Analysis · Mathematics 2018-11-22 Xiaobing Feng , Yukun Li , Yi Zhang

In this paper, we consider flow simulation in highly heterogeneous media that has many practical applications in industry. To enhance mass conservation, we write the elliptic problem in a mixed formulation and introduce a robust two-grid…

Numerical Analysis · Mathematics 2019-05-22 Yanfang Yang , Shubin Fu , Eric T. Chung

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…

Numerical Analysis · Mathematics 2023-10-19 Yan Cheng , Xi Yang

Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set…

Numerical Analysis · Mathematics 2020-05-04 Daniel Jodlbauer , Ulrich Langer , Thomas Wick

We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…

Numerical Analysis · Mathematics 2021-06-09 Andrea Borio , François Hamon , Nicola Castelletto , Joshua A. White , Randolph R. Settgast

Fast computation of demagnetization curves is essential for the computational design of soft magnetic sensors or permanent magnet materials. We show that a sparse preconditioner for a nonlinear conjugate gradient energy minimizer can lead…

Computational Physics · Physics 2018-10-23 Lukas Exl , Johann Fischbacher , Alexander Kovacs , Harald Oezelt , Markus Gusenbauer , Thomas Schrefl

It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…

Numerical Analysis · Mathematics 2022-09-20 Marco Donatelli , Rolf Krause , Mariarosa Mazza , Ken Trotti

We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…

Numerical Analysis · Mathematics 2019-11-15 Hamid Mirchi , Davod Khojasteh Salkuyeh

A combination of block-Jacobi and deflation preconditioning is used to solve a high-order discontinuous element-based collocation discretization of the Schur complement of the Poisson-Neumann system as arises in the operator splitting of…

Numerical Analysis · Mathematics 2016-01-15 Sumedh Joshi , Peter Diamessis

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations.…

Numerical Analysis · Mathematics 2020-02-19 Sriramkrishnan Muralikrishnan , Tan Bui-Thanh , John N. Shadid

A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…

Numerical Analysis · Mathematics 2019-09-04 Chao Chen , Leopold Cambier , Erik G. Boman , Sivasankaran Rajamanickam , Raymond S. Tuminaro , Eric Darve

This paper explores how to adapt a new dynamical core to enable its use in one-way nested regional weather and climate models, where lateral boundary conditions (LBCs) are provided by a lower-resolution driving model. The dynamical core has…