Related papers: Adaptive Mesh Refinement for Characteristic Codes
Sharpness-aware minimization (SAM), which searches for flat minima by min-max optimization, has been shown to be useful in improving model generalization. However, since each SAM update requires computing two gradients, its computational…
In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
The development of novel materials in recent years has been accelerated greatly by the use of computational modelling techniques aimed at elucidating the complex physics controlling microstructure formation in materials, the properties of…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
Sharpness-Aware Minimization (SAM) has proven highly effective in improving model generalization in machine learning tasks. However, SAM employs a fixed hyperparameter associated with the regularization to characterize the sharpness of the…
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement…
This paper proposes an adaptive random experiment design (ARED) algorithm that can be applied to optimize the multiple factors and levels experiments. The algorithm takes real-time model error as the adaptive condition, and outputs a model…
The averaged alternating modified reflections (AAMR) method is a projection algorithm for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method can be seen as an adequate…
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).…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…
This article describes a new, fully adaptive Particle-Multiple-Mesh numerical simulation code developed primarily for simulations of small regions (such as a group of galaxies) in a cosmological context. It integrates the equations of…
We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with the…
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…