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This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…

Numerical Analysis · Mathematics 2024-07-02 Ivan Prusak , Davide Torlo , Monica Nonino , Gianluigi Rozza

High-quality point cloud data is a critical foundation for tasks such as autonomous driving and 3D reconstruction. However, LiDAR-based point cloud acquisition is often affected by various disturbances, resulting in a large number of noise…

Computer Vision and Pattern Recognition · Computer Science 2026-01-06 Ge Zhang , Chunyang Wang , Bin Liu , Guan Xi

In this work, we are concerned with neural network guided goal-oriented a posteriori error estimation and adaptivity using the dual weighted residual method. The primal problem is solved using classical Galerkin finite elements. The adjoint…

Numerical Analysis · Mathematics 2021-02-25 Julian Roth , Max Schröder , Thomas Wick

We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…

Computational Physics · Physics 2016-08-30 Robert Dyja , Baskar Ganapathysubramanian , Kristoffer G. van der Zee

The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to…

Computational Physics · Physics 2025-05-02 Apurva Tiwari , Avijit Chatterjee

We present goal-oriented a posteriori error estimates for the automatic variationally stable finite element (AVS FE) method for scalar-valued convection-diffusion problems. The AVS-FE method is a Petrov-Galerkin method in which the test…

Numerical Analysis · Mathematics 2021-05-12 Eirik Valseth , Albert Romkes

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems [15], [18], this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic…

Optimization and Control · Mathematics 2018-01-09 Randa Herzallah

We present an object-oriented geophysical and astrophysical spectral-element adaptive refinement (GASpAR) code for application to turbulent flows. Like most spectral-element codes, GASpAR combines finite-element efficiency with…

Numerical Analysis · Mathematics 2009-11-11 Duane Rosenberg , Aime' Fournier , Paul Fischer , Annick Pouquet

Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…

Numerical Analysis · Mathematics 2025-03-26 Ying Liu , Jingjing Xiao , Nianyu Yi , Huihui Cao

This paper concerns the adaptive control of a class of discrete-time nonlinear systems with all states accessible. Recently, a high-order tuner algorithm was developed for the minimization of convex loss functions with time-varying…

Optimization and Control · Mathematics 2023-03-21 Peter A. Fisher , Anuradha M. Annaswamy

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties. Here, we generalize the Fourier-space based numerical construction procedure for designing {\it…

Materials Science · Physics 2023-07-27 Wenlong Shi , David Keeney , Duyu Chen , Yang Jiao , Salvatore Torquato

In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. The computation of estimators is simple once corresponding…

Numerical Analysis · Mathematics 2015-03-17 Xiaobo Yin , Hehu Xie

Optimizing space vehicle routing is crucial for critical applications such as on-orbit servicing, constellation deployment, and space debris de-orbiting. Multi-target Rendezvous presents a significant challenge in this domain. This problem…

Systems and Control · Electrical Eng. & Systems 2024-11-19 Antonio López Rivera , Lucrezia Marcovaldi , Jesús Ramírez , Alex Cuenca , David Bermejo

The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…

In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…

Numerical Analysis · Mathematics 2023-09-26 Gouranga Mallik , Thirupathi Gudi

We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…

Numerical Analysis · Mathematics 2025-02-14 Richard Löscher , Michael Reichelt , Olaf Steinbach

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…

Numerical Analysis · Mathematics 2024-01-12 Roland Becker , Gregor Gantner , Michael Innerberger , Dirk Praetorius

Electric vehicles (EVs) have been adopted in urban areas to reduce environmental pollution and global warming as a result of the increasing number of freight vehicles. However, there are still deficiencies in routing the trajectories of…

Artificial Intelligence · Computer Science 2022-06-08 Erick Rodríguez-Esparza , Antonio D Masegosa , Diego Oliva , Enrique Onieva

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable…

Numerical Analysis · Mathematics 2021-02-24 Sergio Rojas , David Pardo , Pouria Behnoudfar , Victor M. Calo

This paper presents an $hp$ a posteriori error analysis for the 2D Helmholtz equation that is robust in the polynomial degree $p$ and the wave number $k$. For the discretization, we consider a discontinuous Galerkin formulation that is…

Numerical Analysis · Mathematics 2019-01-31 Scott Congreve , Joscha Gedicke , Ilaria Perugia