相关论文: Fast multilevel solvers for a class of discrete fo…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…
The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
We consider an efficient preconditioner for boundary integral equation (BIE) formulations of the two-dimensional Stokes equations in porous media. While BIEs are well-suited for resolving the complex porous geometry, they lead to a dense…
We present a comparison of different multigrid approaches for the solution of systems arising from high-order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the…
We study a conservative 5-point cell-centered finite volume discretization of the high-contrast diffusion equation. We aim to construct preconditioners that are robust with respect to the magnitude of the coefficient contrast and the mesh…
In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the…
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss…
We study the performance of a new block preconditioner for a class of $3\times3$ block saddle point problems which arise from finite element methods for solving time-dependent Maxwell equations and some other practical problems. We also…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence…
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.…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi and Gauss-Seidel, or with Krylov methods, e.g., GMRES and…
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…