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In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the…
The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…
This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various…
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with…
In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…
With the emergence of fluid antenna (FA) in wireless communications, the capability to dynamically adjust port positions offers substantial benefits in spatial diversity and spectrum efficiency, which are particularly valuable for mobile…
Graph signal processing deals with algorithms and signal representations that leverage graph structures for multivariate data analysis. Often said graph topology is not readily available and may be time-varying, hence (dynamic) graph…
Adaptive Mesh Refinement (AMR) enables efficient computation of flows by providing high resolution in critical regions while allowing for coarsening in areas where fine detail is unnecessary. While early AMR software packages relied solely…
The fluid antenna system (FAS) refers to a family of reconfigurable antenna technologies that provide substantial spatial gains within a compact, predefined small space, thereby offering extensive degrees of freedom in the physical layer…
Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially-varying density - a limitation that restricts applications in biomedical…
Accurate estimation of the position of network nodes is essential, e.g., in localization, geographic routing, and vehicular networks. Unfortunately, typical positioning techniques based on ranging or on velocity and angular measurements are…
Federated learning (FL) was recently proposed to securely train models with data held over multiple locations (``clients'') under the coordination of a central server. Prolonged training times caused by slow clients may hinder the…
Federated Learning has emerged as a leading paradigm for decentralized, privacy-preserving learning, particularly relevant in the era of interconnected edge devices equipped with sensors. However, the practical implementation of Federated…
This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…
This paper presents a novel constrained Factor Graph Optimization (FGO)-based approach for networked inertial navigation in pedestrian localization. To effectively mitigate the drift inherent in inertial navigation solutions, we incorporate…
We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFEM modifies the classical adaptive finite element method…
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…
This research rigorously investigates the convergence of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in elastic solids. We specifically examine a novel Ambrosio-Tortorelli (AT1)…
We consider an adaptive multiresolution-based lattice Boltzmann scheme, which we have recently introduced and studied from the perspective of the error control and the theory of the equivalent equations. This numerical strategy leads to…