相关论文: Anisotropic space-time goal-oriented error control…
Inference-time alignment for diffusion models aims to adapt a pre-trained reference diffusion model toward a target distribution without retraining the reference score network, thereby preserving the generative capacity of the reference…
We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations (PDEs), adaptive multiresolution (MR) and adaptive mesh refinement (AMR). Both discretizations are based on finite volumes in…
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…
Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can be used to track discontinuities in the…
This paper presents a multi-scale method for convection-dominated diffusion problems in the regime of large P\'eclet numbers. The application of the solution operator to piecewise constant right-hand sides on some arbitrary coarse mesh…
We present a new numerical tool for solving the special relativistic ideal MHD equations that is based on the combination of the following three key features: (i) a one-step ADER discontinuous Galerkin (DG) scheme that allows for an…
We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…
This paper proposes a weight-aware deep reinforcement learning (WADRL) approach designed to address the multiobjective vehicle routing problem with time windows (MOVRPTW), aiming to use a single deep reinforcement learning (DRL) model to…
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…
The space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to simulate non-stationary compressible multicomponent reactive flows. The…
Weight-adjusted inner products are easily invertible approximations to weighted $L^2$ inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time-domain method for wave propagation…
We present a high order one-step ADER-WENO finite volume scheme with space-time adaptive mesh refinement (AMR) for the solution of the special relativistic hydrodynamic and magnetohydrodynamic equations. By adopting a local discontinuous…
This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution by using…
Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy…
Direct Ink Writing (DIW) has gained attention for its potential to reduce printing time and material waste. However, maintaining precise geometry and consistent print quality remains challenging under dynamically varying operating…
We present an accurate and efficient solver for atmospheric dynamics simulations that allows for non-conforming mesh refinement. The model equations are the conservative Euler equations for compressible flows. The numerical method is based…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
We develop reliable a posteriori error estimators for fully discrete Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems endowed with a convex entropy in multiple spatial dimensions on the flat torus…