Related papers: A Micro-Macro parallel-in-time Implementation for …
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
Despite the growing interest in parallel-in-time methods as an approach to accelerate numerical simulations in atmospheric modelling, improving their stability and convergence remains a substantial challenge for their application to…
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
The study deals with the parallelization of 2D and 3D finite element based Navier-Stokes codes using direct solvers. Development of sparse direct solvers using multifrontal solvers has significantly reduced the computational time of direct…
Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…
In this work, we detail the GPU-porting of an in-house pseudo-spectral solver tailored towards large-scale simulations of interface-resolved simulation of drop- and bubble-laden turbulent flows. The code relies on direct numerical…
We present a novel multiscale numerical approach that combines parallel-in-time computation with hybrid domain adaptation for linear collisional kinetic equations in the diffusive regime. The method addresses the computational challenges of…
In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…
A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…
We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In particular, the divergence-free condition and boundary…
A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming…
The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES)…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
A series of benchmarks based on the physical situation of "phase inversion" between two immiscible liquids is presented. These benchmarks aim at progressing toward the direct numerical simulation of two-phase flows. Several CFD codes…
We present a pseudo-spectal Navier-Stokes solver for plane parallel flows (Couette/Poiseuille), that has been developed on the MATLAB programming language. The code performs direct numerical simulations (DNSs) of turbulence in 3 dimensions…
The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine…
We propose a parareal based time parallelization scheme in the phase-space for the particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in kinetic plasma simulations. We use PIF with a coarse tolerance for the…