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In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
Multiresolution provides a fundamental tool based on the wavelet theory to build adaptive numerical schemes for Partial Differential Equations and time-adaptive meshes, allowing for error control. We have introduced this strategy before to…
We consider a hybrid FEM-BEM method to compute approximations of full-space linear elliptic transmission problems. First, we derive a priori and a posteriori error estimates. Then, building on the latter, we present an adaptive algorithm…
The high computational demands of multiscale modeling necessitate advanced parallel and adaptive strategies. To address this challenge, we introduce an adaptive method that utilizes two microscale models based on an offline database for…
In this paper, we study the least-squares finite element methods (LSFEM) for the linear hyperbolic transport equations. The linear transport equation naturally allows discontinuous solutions and discontinuous inflow conditions, while the…
Terahertz (THz) communications have been envisioned as a promising enabler to provide ultra-high data transmission for sixth generation (6G) wireless networks. To tackle the blockage vulnerability brought by severe path attenuation and poor…
Although Federated Learning (FL) is promising to enable collaborative learning among Artificial Intelligence of Things (AIoT) devices, it suffers from the problem of low classification performance due to various heterogeneity factors (e.g.,…
The computational kernel in solving the $S_N$ transport equations is the parallel sweep, which corresponds to directly inverting a block lower triangular linear system that arises in discretizations of the linear transport equation.…
This article deals with the adaptive and approximative computation of the Lam\'e equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM).…
Achieving optimal rates for stochastic composite convex optimization without prior knowledge of problem parameters remains a central challenge. In the deterministic setting, the auto-conditioned fast gradient method has recently been…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
This paper proposes an iterative algorithm for choosing gradient directions use to reconstruct white matter fibers in the brain. The present study is not focusing on data acquisition where scanning is performed. The Adaptive Gradient…
With the widespread adoption of millimeter-wave (mmWave) massive multi-input-multi-output (MIMO) in vehicular networks, accurate beam prediction and alignment have become critical for high-speed data transmission and reliable access. While…
Efficient mobility management techniques are critical in providing seamless connectivity and session continuity between a mobile node and the network during its movement. Current mobility management solutions generally require a central…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
Numerical simulations of flow and transport in porous media usually rely on hybrid-dimensional models, i.e., the fracture is considered as objects of a lower dimension compared to the embedding matrix. Such models are usually combined with…
Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
A large number of problems in computer vision can be modelled as energy minimization problems in a Markov Random Field (MRF) or Conditional Random Field (CRF) framework. Graph-cuts based $\alpha$-expansion is a standard move-making method…
Monotone finite difference methods provide stable convergent discretizations of a class of degenerate elliptic and parabolic Partial Differential Equations (PDEs). These methods are best suited to regular rectangular grids, which leads to…