Related papers: Optimal Response for Hyperbolic Systems by the fas…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
In topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads…
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation…
In this paper we are concerned with rate of convergence of parabolic systems with large diffusion. We will exhibit the exact moment that spatial homogenization occurs and estimate the continuity of attractors by a rate of convergence. We…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…
We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
We study a parabolic system with $p(t,x)$-structure under Dirichlet boundary conditions. In particular, we deduce the optimal convergence rate for the error of the gradient of a finite element based space-time approximation. The error is…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
In this paper, a class of linear parabolic systems of singularly perturbed second order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered. The components of the solution $\vec u$ of…
This paper is devoted to analyzing the observer convergence rate for a class of linear control systems in a Hilbert space. To characterize the polynomial stability of the observer error system, we apply the spectral theory of linear…
Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern…
Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse optimality property since each passivating state feedback controller is optimal with respect to some specific performance index. Due to the nonlinear…
We propose a new analysis of convergence for a $k$th order ($k\ge 1$) finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary value problem. A novel interpolant is introduced, which has…
This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…
We show a linear response statement for fixed points of a family of Markov operators which are perturbations of mixing and regularizing operators. We apply the statement to random dynamical systems on the interval given by a deterministic…