相关论文: Efficient preconditioners for saddle point systems…

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…

We study acceleration and preconditioning strategies for a class of Douglas-Rachford methods aiming at the solution of convex-concave saddle-point problems associated with Fenchel-Rockafellar duality. While the basic iteration converges…

We consider trajectory optimal control problems in which parameter uncertainty limits the applicability of control trajectories computed prior to travel. Hence, efficient trajectory adjustment is needed to ensure successful travel. However,…

To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…

In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. Our findings generalize existing results related to sublinear…

We study preconditioned proximal point methods for a class of saddle point problems, where the preconditioner decouples the overall proximal point method into an alternating primal--dual method. This is akin to the Chambolle--Pock method or…

In this paper we study the linear systems arising from discretized poroelasticity problems. We formulate one block preconditioner for the two-filed Biot model and several preconditioners for the classical three-filed Biot model under the…

The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…

We consider a mixed dimensional elliptic partial differential equation posed in a bulk domain with a large number of embedded interfaces. In particular, we study well-posedness of the problem and regularity of the solution. We also propose…

We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…

We investigate the performance of multigrid preconditioners for solving linear systems arising from finite element discretizations of elliptic interface problems using the Fictitious Domain with Distributed Lagrange Multipliers (FD-DLM)…

This paper presents a study of large linear systems resulting from the regular $B$-splines finite element discretization of the $\bm{curl}-\bm{curl}$ and $\bm{grad}-div$ elliptic problems on unit square/cube domains. We consider systems…

For a Jordan domain with sufficiently smooth boundaries, the solution to the Dirichlet problem for second order skew-symmetric strongly elliptic system with constant coefficients and regular enough boundary data is constructed in the form…

Various natural language processing tasks are structured prediction problems where outputs are constructed with multiple interdependent decisions. Past work has shown that domain knowledge, framed as constraints over the output space, can…

This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…

This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…

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…

Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of…