Related papers: Adaptive Mesh Refinement for Storm Surge
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
We have developed a new computer code, RAM, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. We have implemented a characteristic-wise, finite…
As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…
Storm surge is one of the deadliest hazards posed by tropical cyclones (TCs), yet assessing its current and future risk is difficult due to the phenomenon's rarity and physical complexity. Recent advances in artificial intelligence…
In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries,…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
Accurate time series forecasting is critical for a wide range of problems with temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the…
This contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and…
In recent work we have presented a novel algorithm for mesh refinement which utilizes a reduced model. In particular, the reduced model is used to monitor the transfer of activity (e.g. mass, energy) from larger to smaller scales. When the…
This study investigates the use of machine learning based mesh adaptivity, specifically mesh movement methods (UM2N), with depth integrated non-hydrostatic shallow water models. Motivation for this comes from the need for models which…
We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the…
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…
In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are…
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement…
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…
In this paper, we study the problem of forecasting the next year's number of Atlantic hurricanes, which is relevant in many fields of applications such as land-use planning, hazard mitigation, reinsurance and long-term weather derivative…
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 paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have…
The planning and operation of renewable energy, especially wind power, depend crucially on accurate, timely, and high-resolution weather information. Coarse-grid global numerical weather forecasts are typically downscaled to meet these…