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Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…

Numerical Analysis · Mathematics 2015-03-17 Weizhang Huang , Lennard Kamenski , Xianping Li

This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…

Numerical Analysis · Mathematics 2025-08-27 Markus Bachmayr , Simon Boisserée

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being…

Numerical Analysis · Mathematics 2015-03-19 Xiaobo Yin , Hehu Xie

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

Optimization and Control · Mathematics 2025-12-12 Chenglong Bao , Yancheng Yuan , Shulan Zhu

We present an $rp$-adaptation strategy for high-fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser to $r$-adapt the mesh and…

Computational Physics · Physics 2020-11-10 Julian Marcon , Giacomo Castiglioni , David Moxey , Spencer J. Sherwin , Joaquim Peiró

Adaptive finite elements are the method of choice for accurate simulations of optical components. However as shown recently by Bienstman et al. many finite element mode solvers fail to compute the propagation constant's imaginary part of a…

Optics · Physics 2009-05-28 L. Zschiedrich , S. Burger , J. Pomplun , F. Schmidt

It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently…

Optimization and Control · Mathematics 2024-02-02 Cristian Daniel Alecsa

The paper describes a receding horizon control design framework for continuous-time stochastic nonlinear systems subject to probabilistic state constraints. The intention is to derive solutions that are implementable in real-time on…

Systems and Control · Computer Science 2012-11-20 Shridhar K. Shah , Herbert G. Tanner , Chetan D. Pahlajani

Anisotropic mesh adaptation is studied for the linear finite element solution of eigenvalue problems with anisotropic diffusion operators. The M-uniform mesh approach is employed with which any nonuniform mesh is characterized…

Numerical Analysis · Mathematics 2020-04-20 Jingyue Wang , Weizhang Huang

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…

Optimization and Control · Mathematics 2014-10-17 Stefan Streif , Matthias Karl , Ali Mesbah

High precision measurements are essential to solve major scientific and technological challenges, from gravitational wave detection to healthcare diagnostics. Quantum sensing delivers greater precision, but an in-depth optimisation of…

Boltzmann transport problems often involve heavy streaming, where particles propagate long distance due to the dominance of advection over particle interaction. If an insufficiently refined non-rotationally invariant angular discretisation…

Numerical Analysis · Mathematics 2019-11-06 S. Dargaville , R. P. Smedley-Stevenson , P. N. Smith , C. C. Pain

This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalised by the relative entropy. We identify suitable metric space on which we construct a gradient flow for the…

Optimization and Control · Mathematics 2024-01-26 David Šiška , Łukasz Szpruch

A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…

Numerical Analysis · Mathematics 2011-08-24 Qingshan Chen , Max Gunzburger

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Optimization and Control · Mathematics 2026-02-17 Patrick L. Combettes , Javier I. Madariaga

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…

Optimization and Control · Mathematics 2020-05-29 Rohit Kannan , James Luedtke

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints.We investigate the…

Optimization and Control · Mathematics 2025-04-01 Caroline Geiersbach , Tim Suchan , Kathrin Welker

A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…

Numerical Analysis · Mathematics 2017-02-01 Pia Domschke , Aseem Dua , Jeroen J. Stolwijk , Jens Lang , Volker Mehrmann

We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…

Optimization and Control · Mathematics 2026-03-10 Mickael Binois , Jeffrey Larson

Anisotropic mesh adaptation with Riemannian metrics has proven effective for generating straight-sided meshes with anisotropy induced by the geometry of interest and/or the resolved physics. Within the continuous mesh framework, anisotropic…

Numerical Analysis · Mathematics 2025-01-14 Arthur Bawin , André Garon , Jean-François Remacle