Related papers: GPU Accelerated Explicit Time Integration Methods …
Splitting-based time integration approaches such as fractional steps, alternating direction implicit, operator splitting, and locally one-dimensional methods partition the system of interest into components and solve individual components…
We consider a Runge--Kutta method for the numerical time integration of the nonstationary incompressible Navier--Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge--Kutta method. The…
We present a GPU parallel implementation of the numeric integration of the Vlasov equation in one spatial dimension based on a second order time-split algorithm with a local modified cubic-spline interpolation. We apply our approach to…
The use of high order fully implicit Runge-Kutta methods is of significant importance in the context of the numerical solution of transient partial differential equations, in particular when solving large scale problems due to fine space…
This paper explores two condensed-space interior-point methods to efficiently solve large-scale nonlinear programs on graphics processing units (GPUs). The interior-point method solves a sequence of symmetric indefinite linear systems, or…
A third-order accurate implicit-explicit Runge-Kutta time marching numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with arbitrary damping…
Irksome is a library based on the Unified Form Language (UFL) that automates the application of Runge-Kutta time-stepping methods for finite element spatial discretizations of partial differential equations (PDEs). This paper describes…
In this thesis we develop techniques to efficiently solve numerical Partial Differential Equations (PDEs) using Graphical Processing Units (GPUs). Focus is put on both performance and re--usability of the methods developed, to this end a…
We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…
Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of timescales, and where the relative importance of these processes often varies by…
We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge--Kutta--Legendre (RKL) and Runge--Kutta--Gegenbauer (RKG) super-time-stepping methods were…
Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit…
To solve the Cahn-Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the…
The task of integrating a large number of independent ODE systems arises in various scientific and engineering areas. For nonstiff systems, common explicit integration algorithms can be used on GPUs, where individual GPU threads…
We present in this paper algorithms for solving stiff PDEs on the unit sphere with spectral accuracy in space and fourth-order accuracy in time. These are based on a variant of the double Fourier sphere method in coefficient space with…
We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations discretized on staggered (MAC) grids. The scheme is based on finite difference approximations…
Implicit Runge--Kutta (IRK) methods are highly effective for solving stiff ordinary differential equations (ODEs) but can be computationally expensive for large-scale problems due to the need of solving coupled algebraic equations at each…
We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes…
Fully implicit timestepping methods have several potential advantages for atmosphere/ocean simulation. First, being unconditionally stable, they degrade more gracefully as the Courant number increases, typically requiring more solver…