相关论文: High-Order Mesh r-Adaptivity with Tangential Relax…

In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…

We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a…

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…

We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…

As language models scale to trillions of parameters, distributed training across many GPUs becomes essential, yet gradient synchronization over high-bandwidth, low-latency networks remains a critical bottleneck. While recent methods like…

In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the…

Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the…

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…

In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion…

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…

Soft robotics has emerged as the standard solution for grasping deformable objects, and has proven invaluable for mobile robotic exploration in extreme environments. However, despite this growth, there are no widely adopted computational…

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…

The multiscale nature of turbulent combustion necessitates accurate and computationally efficient methods for direct numerical simulations (DNS). The field has long been dominated by high-order finite differences, which lack the flexibility…

This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…

Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines)…