Related papers: A Comparison of Two Shallow Water Models with Non-…
We propose an Adaptive Perfectly Matched Layer (APML) to be used in diffraction grating modeling. With a properly tailored co-ordinate stretching depending both on the incident field and on grating parameters, the APML may efficiently…
The implementation and validation of the adaptive buffered force QM/MM method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for…
This paper explores static non-uniform grid solvers that adapt three raster-based flood models on an optimised non-uniform grid: the second-order discontinuous Galerkin (DG2) model representing the modelled data as piecewise-planar fields,…
Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
Lattice Boltzmann Methods (LBM) stand out for their simplicity and computational efficiency while offering the possibility of simulating complex phenomena. While they are optimal for Cartesian meshes, adapted meshes have traditionally been…
This work presents an optimization framework for tailoring the nonlinear dynamic response of lightly damped mechanical systems using Spectral Submanifold (SSM) reduction. We derive the SSM-based backbone curve and its sensitivity with…
Hyperspectral imagery collected from airborne or satellite sources inevitably suffers from spectral variability, making it difficult for spectral unmixing to accurately estimate abundance maps. The classical unmixing model, the linear…
We present an object-oriented geophysical and astrophysical spectral-element adaptive refinement (GASpAR) code for application to turbulent flows. Like most spectral-element codes, GASpAR combines finite-element efficiency with…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
This report summarizes the major progresses to develop the dynamic core for next-generation atmospherical model for both numerical weather prediction and climate simulation. The numerical framework is based on a general formulation,…
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…
An adaptive modeling method (AMM) that couples a deep neural network potential and a classical force field is introduced to address the accuracy-efficiency dilemma faced by the molecular simulation community. The AMM simulated system is…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
We propose a new unstructured numerical subgrid method for solving the shallow water equations using a finite volume method with enhanced bathymetry resolution. The method employs an unstructured triangular mesh with support for…
Global climate models parameterize a range of atmospheric-oceanic processes like gravity waves, clouds, moist convection, and turbulence that cannot be sufficiently resolved. These subgrid-scale closures for unresolved processes are a…
Benefiting from the vigorous development of deep learning, many CNN-based image super-resolution methods have emerged and achieved better results than traditional algorithms. However, it is difficult for most algorithms to adaptively adjust…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…