相关论文: Iterated quasi-reversibility method applied to ell…

In this article we investigate the existence of a solution to a semilinear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one…

In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of two different piecewise constant coefficients in an elliptic partial differential equation. We show that the Bayesian formulation of…

We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…

We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…

In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the…

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…

In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted…

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…

We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…

We consider data assimilation for the heat equation using a finite element space semi-discretization. The approach is optimization based, but the design of regularization operators and parameters rely on techniques from the theory of…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…

The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…

Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…

In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem}(or cell problem), i.e. we…

Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…