The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather prediction (NWP), is addressed. Parallel-in-time schemes are a possible way to increase, on the algorithmic level, the amount of parallelism, a requirement arisin...

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there high contrast changes media properties. For solving these problems, one often uses coarse spatial grid for resolution. temporal discretization, implicit methods used. methods, though the step can be relatively large, difficult to compute due nonlinearity fact that de...

We consider Sundman and Poincaré transformations for the long-time numerical integration of Hamiltonian systems whose evolution occurs at different time scales. The transformed systems are numerically integrated using explicit symplectic methods. The schemes we consider are explicit symplectic methods with adaptive time steps and they generalise other methods from the literature, while exhibiti...

This paper discusses the design and implementation of solution algorithms suitable for performing transient, incompressible viscous ow simulations on massively parallel computers. The nite element formulation for incompressible ow along with the ad-hoc modi cations for explicit time integration are discussed with an emphasis on implementation aspects for achieving scalable, parallel computation...

The stability and accuracy of the Generalized Interpolation Material Point (GIMP) Method is measured directly through carefully-formulated manufactured solutions over wide ranges of CFL numbers and mesh sizes. The manufactured solutions are described in detail. The accuracy and stability of several time integration schemes are compared via numerical experiments. The effect of various treatment ...

A nonstiff additive semi-implicit third-order Runge-Kutta scheme suitable for integration of convection-diffusion-reaction equations with few diffusion dominated species is presented in this article. This scheme permits larger time steps than those required by explicit schemes and uses only one implicit stage and two explicit stages. The stability domain is analyzed and tests are carried out fo...

A new explicit time-reversible orbit integrator for the equations of motion in a static homogeneous magnetic field —called Cyclotronic integrator— is presented. Like Spreiter and Walter’s Taylor expansion algorithm, for sufficiently weak electric field gradients this second order method does not require a fine resolution of the Larmor motion; it has however the essential advantage of being symp...

A high-order implicit-explicit additive Rung-Kutta time integrator is implemented in a particle-in-cell method based on a high-order discontinuous Galerkin Maxwell solver for simulation of plasmas. The method satisfies Gauss law using a hyperbolic divergence cleaner that transports divergence out of the computational domain at several times the speed of light. The stiffness in the field equatio...

We have introduced a fully second order IMplicit/EXplicit (IMEX) time integration technique for solving the compressible Euler equations plus nonlinear heat conduction problems (also known as the radiation hydrodynamics problems) in Kadioglu et al., J. Comp. Physics [22, 24]. In this paper, we study the implications when this method is applied to the incompressible Navier-Stokes (N-S) equations...