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A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We propose an efficient algorithm to numerically solve Anderson impurity problems using matrix product states. By introducing a modified chain mapping we obtain significantly lower entanglement, as compared to all previous attempts, while…
The Dirac-Frenkel time-dependent variational approach with Davydov Ans\"atze is a sophisticated, yet efficient technique to obtain an acuurate solution to many-body Schr\"odinger equations for energy and charge transfer dy- namics in…
Most of today's state-of-the-art methods for perspective shape from shading are modelled in terms of partial differential equations (PDEs) of Hamilton-Jacobi type. To improve the robustness of such methods w.r.t. noise and missing data,…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
We use the numerical renormalization group method to study an Anderson impurity in a conduction band with the density of states varying as rho(omega) \propto |omega|^r with r>0. We find two different fixed points: a local-moment fixed point…
We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they…
We study the real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small…
A dynamic density-matrix renormalisation group approach to the spectral properties of quantum impurity problems is presented. The method is demonstrated on the spectral density of the flat-band symmetric single-impurity Anderson model. We…
We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely, matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level…
We develop analytical tools and numerical methods for time evolving the total density matrix of the finite-size Anderson model. The model is composed of two finite metal grains, each prepared in canonical states of differing chemical…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
In this paper, we present a fast and effective method for solving the Poisson-modified total variation model proposed in [9]. The existence and uniqueness of the model are again proved using different method. A semi-implicit difference…
We present a deterministic algorithm for the efficient evaluation of imaginary time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. In addition to the efficient…
We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…
Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…