相关论文: Inexact Solves in Interpolatory Model Reduction

In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once…

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

The Iterative Rational Krylov Algorithm (IRKA) of [8] is an interpolatory model reduction approach to the optimal $\mathcal{H}_2$ approximation problem. Even though the method has been illustrated to show rapid convergence in various…

The main goal of this paper is to investigate the order reduction phenomenon that appears in the integral deferred correction (InDC) methods based on implicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class of stiff…

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…

One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…

We develop and analyze an inexact regularized alternating projection method for nonconvex feasibility problems. Such a method employs inexact projections on one of the two sets, according to a set of well-defined conditions. We prove the…

We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…

Galerkin and Petrov-Galerkin methods are some of the most successful solution procedures in numerical analysis. Their popularity is mainly due to the optimality properties of their approximate solution. We show that these features carry…

We develop a Petrov-Galerkin stabilization method for multiscale convection-diffusion transport systems. Existing stabilization techniques add a limited number of degrees of freedom in the form of bubble functions or a modified diffusion,…

We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method…

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential…

For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…

The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…

The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…

An effective approach for construction of simple approximation for description of non-ideality effects in classical one- and two-component plasma model is under discussion. General constraints i.e. positiveness and exponential type for…