Related papers: Performance analysis of high-resolution ice sheet …
The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…
This paper describes the first steps of development of a new multidimensional time implicit code devoted to the study of hydrodynamical processes in stellar interiors. The code solves the hydrodynamical equations in spherical geometry and…
We present a multi-level elastodynamics timestep solver for accelerating incremental potential contact (IPC) simulations. Our method retains the robustness of gold standard IPC in the face of intricate geometry, complex heterogeneous…
Grid adaptation for implicit Large Eddy Simulation (LES) is a non-trivial challenge due to the inherent coupling of the modeling and numerical errors. An attempt to address the challenge first requires a comprehensive assessment and then…
At the heart of the Met Office climate and weather forecasting capabilities lies a sophisticated numerical model which solves the equations of large-scale atmospheric flow. Since this model uses semi-implicit time-stepping, it requires the…
The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…
We present recent advances on the massively parallel performance of a numerical scheme for atmosphere dynamics applications based on the deal.II library. The implicit-explicit discontinuous finite element scheme is based on a matrix-free…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
We examine the nature of the ice-albedo feedback in a long standing approach used in the dynamic-thermodynamic modeling of sea ice. The central issue examined is how the evolution of the ice area is treated when modeling a partial ice cover…
We systematically validate the static local mesh refinement capabilities of a recently proposed IMEX-DG scheme implemented in the framework of the deal.II library. Non-conforming meshes are employed in atmospheric flow simulations to…
We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In keeping with the literature we study a class of initial…
Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers which seem sufficiently accurate for the forward…
Arctic sea ice is rapidly retreating due to global warming, and emerging evidence suggests that the rate of decline may have been underestimated. A key factor contributing to this underestimation is the coarse resolution of current climate…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
Purpose - This paper continues the development of a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling. Design/methodology/approach - A front-tracking/finite volume method introduced in Part I…
Semi-implicit time-stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision…
Coupled natural systems are generally modeled at multiple abstraction levels. Both structural scale and behavioral complexity of these models are determinants in the kinds of questions that can be posed and answered. As scale and complexity…
In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…