Related papers: Adaptive Mesh Refinement for Variational Inequalit…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a…
Adaptive mesh refinement is central to the efficient solution of partial differential equations (PDEs) via the finite element method (FEM). Classical $r$-adaptivity optimizes vertex positions but requires solving expensive auxiliary PDEs…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
The mesh flexibility offered by the virtual element method through the permission of arbitrary element geometries, and the seamless incorporation of `hanging' nodes, has made the method increasingly attractive in the context of adaptive…
We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…
The problem of the resolution of turbulent flows in adaptive mesh refinement (AMR) simulations is investigated by means of 3D hydrodynamical simulations in an idealised setup, representing a moving subcluster during a merger event. AMR…
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…
This paper presents an advancement to an approach for model-independent surrogate-based optimization with adaptive batch sampling, known as Adaptive Model Refinement (AMR). While the original AMR method provides unique decisions with…
We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the…
Due to scarcity of anomaly situations in the early manufacturing stage, an unsupervised anomaly detection (UAD) approach is widely adopted which only uses normal samples for training. This approach is based on the assumption that the…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
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…
We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called…
For the non-conforming Crouzeix-Raviart boundary elements from [Heuer, Sayas: Crouzeix-Raviart boundary elements, Numer. Math. 112, 2009], we develop and analyze a posteriori error estimators based on the $h-h/2$ methodology. We discuss the…
In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used element type,…
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…
The realization of a standard Adaptive Finite Element Method (AFEM) preserves the mesh conformity by performing a completion step in the refinement loop: in addition to elements marked for refinement due to their contribution to the global…