相关论文: Multigrid solvers for isogeometric discretizations…
This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…
Bilevel optimization has arisen as a powerful tool in modern machine learning. However, due to the nested structure of bilevel optimization, even gradient-based methods require second-order derivative approximations via Jacobian- or/and…
In this paper, we investigate inexact variants of dual-primal isogeometric tearing and interconnecting methods for solving large-scale systems of linear equations arising from Galerkin isogeometric discretizations of elliptic boundary value…
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
We investigate and derive second solutions to linear homogeneous second-order difference equations using a variety of methods, in each case going beyond the purely formal solution and giving explicit expressions for the second solution. We…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd…
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…
A stabilized Lagrange multiplier method for second order elliptic interface problems is presented in the framework of mortar method. The requirement of LBB (Ladyzhenskaya-Babu\v{s}ka-Brezzi) condition for mortar method is alleviated by…
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the…
In this paper, we consider a classical form of optimal algebraic multigrid (AMG) interpolation that directly minimizes the two-grid convergence rate and compare it with the so-called ideal form that minimizes a certain weak approximation…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…
Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD) linear systems resulting from the discretization of general elliptic PDEs, or the spatial discretization of parabolic PDEs. However, convergence…
We continue our study [Domain Uncertainty Quantification in Computational Electromagnetics, JUQ (2020), 8:301--341] of the numerical approximation of time-harmonic electromagnetic fields for the Maxwell lossy cavity problem for uncertain…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…