Related papers: Adaptive Mesh Refinement for Characteristic Grids
This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population…
We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…
In this paper we extend the recently developed third-order limiter function $H_{3\text{L}}^{(c)}$ [J. Sci. Comput., (2016), 68(2), pp.~624--652] to make it applicable for more elaborate test cases in the context of finite volume schemes.…
Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…
Current Adaptive Mesh Refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient…
High-order solvers for compressible flows are vital in scientific applications. Adaptive mesh refinement (AMR) is a key technique for reducing computational cost by concentrating resolution in regions of interest. In this work, we develop…
Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…
Gravitational instabilities naturally give rise to multi-scale structure, which is difficult for traditional Eulerian hydrodynamic methods to accurately evolve. This can be circumvented by adaptively adding resolution (in the form of…
Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…
Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS…
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 an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
The call for efficient computer architectures has introduced a variety of application-specific compute engines to the heterogeneous computing landscape. One particular engine, the analog mesh computer, has been well received due to its…
In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used element type,…
Retrieval-Augmented Generation (RAG), by integrating non-parametric knowledge from external knowledge bases into models, has emerged as a promising approach to enhancing response accuracy while mitigating factual errors and hallucinations.…
Block-structured AMR meshes are often used in astrophysical fluid simulations, where the geometry of the domain is simple. We consider potential efficiency gains for time sub-cycling, or time refinement (TR), on Berger-Collela and oct-tree…