Related papers: A uniform preconditioner for a Newton algorithm fo…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear…
We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle…
In this work, we propose a simple yet generic preconditioned Krylov subspace method for a large class of nonsymmetric block Toeplitz all-at-once systems arising from discretizing evolutionary partial differential equations. Namely, our main…
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…
In this paper we study the relaxed primal-dual algorithm for solving composite monotone inclusions in real Hilbert spaces with critical preconditioners. Our approach is based in new results on the asymptotic behaviour of…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error. Often, such systems arise from the discretization of operator…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
The focus of this work is on the construction and analysis of optimal-order multigrid preconditioners to be used in the Newton-Krylov method for a distributed optimal control problem constrained by the stationary Navier-Stokes equations. As…
The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…
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 propose a new image restoration model based on the minimized surface regularization. The proposed model closely relates to the classical smoothing ROF model \cite{4}. We can reformulate the proposed model as a min-max problem and solve…
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous…
In this paper, we devise a $\operatorname{prox}$-based semi-smooth Newton method for the non-differentiable TV-minimization problem. To this end, the primal-dual optimality conditions are reformulated as a nonlinear operator equation with…
A novel theoretical convergence rate estimate for a Balancing Domain Decomposition by Constraints algorithm is proven for the solution of the cardiac Bidomain model, describing the propagation of the electric impulse in the cardiac tissue.…
The solution of matrices with $2\times 2$ block structure arises in numerous areas of computational mathematics, such as PDE discretizations based on mixed-finite element methods, constrained optimization problems, or the implicit or steady…
A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general source allows for quasi-best approximation with lowest-order finite element methods. This paper establishes the stability and a priori error…