Related papers: A Framework for the Solution of Tree-Coupled Saddl…
When solving linear systems with nonsymmetric Toeplitz or multilevel Toeplitz matrices using Krylov subspace methods, the coefficient matrix may be symmetrized. The preconditioned MINRES method can then be applied to this symmetrized…
We present families of space-time finite element methods (STFEMs) for a coupled hyperbolic-parabolic system of poro- or thermoelasticity. Well-posedness of the discrete problems is proved. Higher order approximations inheriting most of the…
We propose a Nested BDDC for a class of saddle-point problems. The method solves for both flux and pressure variables. The fluxes are resolved in three-steps: the coarse solve is followed by subdomain solves, and last we look for a…
Large linear systems of saddle-point type have arisen in a wide variety of applications throughout computational science and engineering. The discretizations of distributed control problems have a saddle-point structure. The numerical…
For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…
Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \cite{G1, G2}, we propose new templates for solving large non-symmetric linear systems. The…
In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a…
We investigate various block preconditioners for a low-order Raviart-Thomas discretization of the mixed Poisson problem on adaptive quadrilateral meshes. In addition to standard diagonal and Schur complement preconditioners, we present a…
We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We…
We introduce a robust and efficient preconditioner for a hybrid Newton-GMRES method for solving the nonlinear systems arising from incompressible Navier-Stokes equations. When the Reynolds number is relatively high, these systems often…
Design optimization and uncertainty quantification, among other applications of industrial interest, require fast or multiple queries of some parametric model. The Proper Generalized Decomposition (PGD) provides a separable solution, a…
In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional…
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
Saddle points provide a hierarchical view of the energy landscape, revealing transition pathways and interconnected basins of attraction, and offering insight into the global structure, metastability, and possible collective mechanisms of…