Related papers: Implicit Adaptive Mesh Refinement for Dispersive T…
We present a high-order entropy stable discontinuous Galerkin (ESDG) method for the two dimensional shallow water equations (SWE) on curved triangular meshes. The presented scheme preserves a semi-discrete entropy inequality and remains…
We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with extremely high resolution. Our method utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids…
We propose an implicit Discontinuous Galerkin (DG) discretization for incompressible two-phase flows using an artificial compressibility formulation. The conservative level set (CLS) method is employed in combination with a reinitialization…
This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, which makes adaptivity essential in improving the simulation…
In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order…
Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models…
Accurate 3D reconstruction in degraded imaging conditions remains a key challenge in photogrammetry and neural rendering. In underwater environments, spatially varying visibility caused by scattering, attenuation, and sparse observations…
We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…
A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of…
We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…
Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with…
We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…
We present REMIX, a smoothed particle hydrodynamics (SPH) scheme designed to alleviate effects that typically suppress mixing and instability growth at density discontinuities in SPH simulations. We approach this problem by directly…
Permeability estimation of porous media from direct solving Navier--Stokes equation has a wide spectrum of applications in petroleum industry. In this paper, we utilize a pressure-correction projection algorithm in conjunction with the…
We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a…
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…
Efficient time integration schemes are necessary to capture the complex processes involved in atmospheric flows over long periods of time. In this work, we propose a high-order, implicit-explicit numerical scheme that combines Multi-Level…
A non-negativity-preserving cut-cell discontinuous Galerkin method for the degenerate parabolic diffusive wave approximation of the shallow water equation is presented. The method can handle continuous and discontinuous bathymmetry as well…
In this work, by introducing the seismic impedance tensor we propose a new Rayleigh wave dispersion function in a homogeneous and layered medium of the Earth, which provides an efficient way to compute the dispersion curve -- a relation…
We present the massively parallel performance of a $h$-adaptive solver for atmosphere dynamics that allows for non-conforming mesh refinement. The numerical method is based on a Discontinuous Galerkin (DG) spatial discretization, highly…