Related papers: Further development of efficient and accurate time…
Recent advancements in evaluating matrix-exponential functions have opened the doors to the practical use of exponential time-integration methods in numerical weather prediction (NWP). The success of exponential methods in shallow water…
High-performance computing trends towards many-core systems are expected to continue over the next decade. As a result, parallel-in-time methods, mathematical formulations which exploit additional degrees of parallelism in the time…
We introduce a class of explicit exponential Rosenbrock methods for the time integration of large systems of stiff differential equations. Their application with respect to simulation tasks in the field of visual computing is discussed…
Cloud and precipitation microphysics packages in atmospheric general circulation models typically use first-order time integration methods with a large time step, requiring ad hoc limiters and substepping of the sedimentation scheme to…
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…
Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…
In this paper we propose a novel class of methods for high order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the…
Non-hydrostatic atmospheric models often use semi-implicit temporal discretisations in order to negate the time step limitation of explicitly resolving the fast acoustic and gravity waves. Solving the resulting system to machine precision…
In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…
Simulation of geothermal systems is challenging due to coupled physical processes in highly heterogeneous media. Combining the exponential Rosenbrock--Euler and Rosenbrock-type methods with control-volume (two-point flux approximation)…
Time integration of advection dominated advection-diffusion problems on refined meshes can be a challenging task, since local refinement can lead to a severe time step restriction, whereas standard implicit time stepping is usually hardly…
Exponential time integrators have been applied successfully in several physics-related differential equations. However, their application in hyperbolic systems with absorbing boundaries, like the ones arising in seismic imaging, still lacks…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
Computational chemical combustion problems are known to be stiff, and are typically solved with implicit time integration methods. A novel exponential time integrator, EPI3V, is introduced and applied to a spatially homogeneous isobaric…
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…
The structural flexibility of the exponential propagation iterative methods of Runge-Kutta type (EPIRK) enables construction of particularly efficient exponential time integrators. While the EPIRK methods have been shown to perform well on…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time…