相关论文: Increasing stable time-step sizes of the free-surf…

We present the Thickness Stabilization Scheme (TSS), a numerical stabilization scheme suitable for the Shallow Shelf Approximation (SSA), one of the most widely-used models for large-scale Antarctic and Greenland ice sheet simulations. The…

The Shallow Ice Approximation (SIA) model on strong form is commonly used for inferring the flow dynamics of grounded ice sheets. The solution to the SIA model is a closed-form expression for the velocity field. When that velocity field is…

Numerical ice sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or…

Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…

We propose and implement a new method, called the Ice Sheet Coupled Approximation Levels (ISCAL) method, for simulation of ice sheet flow in large domains under long time-intervals. The method couples the exact, full Stokes (FS) equations…

This manuscript introduces an advanced numerical approach for the integration of incompressible Navier-Stokes (NS) equations using a Time Series Expansion (TSE) method within a Finite Element Method (FEM) framework. The technique is…

In this paper we introduce adaptive time step control for simulation of evolution of ice sheets. The discretization error in the approximations is estimated using "Milne's device" by comparing the result from two different methods in a…

We investigate the accuracy and robustness of one of the most common methods used in glaciology for the discretization of the $\mathfrak{p}$-Stokes equations: equal order finite elements with Galerkin Least-Squares (GLS) stabilization.…

Phase transition in its strict sense can only be observed in an infinite system, for which equilibration takes an infinitely long time at criticality. In numerical simulations, we are often limited both by the finiteness of the system size…

The velocity field and the height at the surface of a dynamic ice sheet are observed. The ice sheets are modeled by the full Stokes equations and shallow shelf/shelfy stream approximations. Time dependence is introduced by a kinematic free…

The primary data which determine the evolution of glaciation are the bedrock elevation and the surface mass balance. From this data, which we assume is defined over a fixed land region, the glacier's geometry solves a free boundary problem…

The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

Forecast verification plays a crucial role in the development cycle of operational numerical weather prediction models. At the same time, verification remains a challenge as the traditionally used non-spatial forecast quality metrics…

This report considers a variable step time discretization algorithm proposed by Dahlquist, Liniger and Nevanlinna and applies the algorithm to the unsteady Stokes/Darcy model. Although long-time forgotten and little explored, the algorithm…

Temperature stabilization of oil and gas wells is used to ensure stability and prevent deformation of a subgrade estuary zone. In this work, we consider the numerical simulation of thermal stabilization using vertical seasonal freezing…

We provide a comprehensive view of various phase transitions in random $K$-satisfiability problems solved by stochastic-local-search algorithms. In particular, we focus on the finite-size scaling (FSS) exponent, which is mathematically…

A stabilized finite element method is introduced for the simulation of time-periodic creeping flows, such as those found in the cardiorespiratory systems. The new technique, which is formulated in the frequency rather than time domain,…

A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…

Modeling time series is a research focus in cryospheric sciences because of the complexity and multiscale nature of events of interest. Highly non-uniform sampling of measurements from different sensors with different levels of accuracy, as…