相关论文: A phase-field approach for the interface reconstru…

In this work, we investigate the numerical reconstruction of inclusions in a semilinear elliptic equation arising in the mathematical modeling of cardiac ischemia. We propose an adaptive finite element method for the resulting constrained…

In this paper, we deal with the problem of determining perfectly insulating regions (cavities) from one boundary measurement in a nonlinear elliptic equation arising from cardiac electrophysiology. Based on the results obtained in [9] we…

In this paper, we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's measurements. For, we consider a constrained minimization…

We propose a double obstacle phase field approach to the recovery of piece-wise constant diffusion coefficients for elliptic partial differential equations. The approach to this inverse problem is that of optimal control in which we have a…

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection…

We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a…

We deal with the geometrical inverse problem of the shape reconstruction of cavities in a bounded linear isotropic medium by means of boundary data. The problem is addressed from the point of view of optimal control: the goal is to minimize…

This paper deals with the local recovery of conservative fluxes for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed weakly and the discretisation is achieved by using…

We investigate a phase-field version of the Faber--Krahn theorem based on a phase-field optimization problem introduced in Garcke et al. [ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 10] formulated for the principal eigenvalue of…

In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…

In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods…

A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method…

One of the challenges in phase measuring deflectometry is to retrieve the wavefront from objects that present discontinuities or non-differentiable gradient fields. Here, we propose the integration of such gradients fields based on an…

This paper investigates an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes, employing the CutFEM method. The main contribution is the a posteriori error analysis based on equilibrated fluxes belonging…

We advance a combined filtered/phase-field approach to topology optimization in the setting of linearized elasticity. Existence of minimizers is proved and rigorous parameter asymptotics are discussed by means of variational convergence…

The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…

We numerically implement the variational approach for reconstruction in the inverse crack and cavity problems developed by one of the authors. The method is based on a suitably adapted free-discontinuity problem. Its main features are the…

We propose and analyze an unfitted finite element method for solving elliptic problems on domains with curved boundaries and interfaces. The approximation space on the whole domain is obtained by the direct extension of the finite element…

We investigate the problem of finding the optimal shape and topology of a system of acoustic lenses in a dissipative medium. The sound propagation is governed by a general semilinear strongly damped wave equation. We introduce a phase-field…

In this paper, we develop an efficient preconditioned unfitted finite element method for the elliptic interface problem, based on the reconstructed discontinuous approximation. The approximation method for interface problems is originally…