Related papers: Numerical Reconstruction of Coefficients in Ellipt…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…
In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting…
We study the inverse problem of determining uniquely and stably quasilinear terms appearing in an elliptic equation from boundary excitations and measurements associated with the solutions of the corresponding equation. More precisely, we…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
We introduce and study the Dirichlet problem for double divergence form elliptic equations with coefficients of low regularity and boundary conditions given by general Borel measures. Under broad assumptions we establish the solvability of…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
We consider the Dirichlet problem for elliptic systems with periodically distributed inclusions whose conduction parameter exhibits a significant contrast compared to the background media. We develop a unified method to quantify the…
In this paper we present a methodology that allows the efficient computation of the topological derivative for semilinear elliptic problems within the averaged adjoint Lagrangian framework. The generality of our approach should also allow…
Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the…
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional…
We consider the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calder\'on's problem. In a previous result by the authors on monotonicity-based reconstruction, the perturbed coefficient is…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
This work considers the reconstruction of a space-dependent potential from boundary observations in subdiffusion by a stable and robust recovery method. Specifically, we develop an algorithm to minimize the Kohn-Vogelius cost function,…
Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in…
We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$. Under the…
We generalize and analyse the method for computing lower bounds of the principal eigenvalue proposed in our previous paper (I. Sebestova, T. Vejchodsky, SIAM J. Numer. Anal. 2014). This method is suitable for symmetric elliptic eigenvalue…
We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…