Related papers: Tree-based adaptive finite element methods for def…
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…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error…
Deformation field estimation is an important and challenging issue in many medical image registration applications. In recent years, deep learning technique has become a promising approach for simplifying registration problems, and has been…
We present the analytical formulation and the finite element solution of a fractional-order nonlocal continuum model of a Euler-Bernoulli beam. Employing consistent definitions for the fractional-order kinematic relations, the governing…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
Evaluating deformable image registration (DIR) is challenging due to the inherent trade-off between achieving high alignment accuracy and maintaining deformation regularity. However, most existing DIR works either address this trade-off…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
We consider a mixed variational formulation recently proposed for the coupling of the Brinkman--Forchheimer and Darcy equations and develop the first reliable and efficient residual-based a posteriori error estimator for the 2D version of…
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…
We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…
In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver better accuracy due…
Objective: In medical imaging, it is often crucial to accurately assess and correct movement during image-guided therapy. Deformable image registration (DIR) consists in estimating the required spatial transformation to align a moving image…
In this work, we develop an adaptive nonconforming finite element algorithm for the numerical approximation of phase-field parameterized topology optimization governed by the Stokes system. We employ the conforming linear finite element…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…