We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...
We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...
We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...
PERMON (Parallel, Efficient, Robust, Modular, Object-oriented, Numerical) is a newly emerging collection of software libraries, uniquely combining Quadratic Programming (QP) algorithms and Domain Decomposition Methods (DDM). Among the main applications are contact problems of mechanics. This paper gives an overview of PERMON and selected ingredients improving scalability, demonstrated by numerical experiments.
In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive...
In this paper, we
investigate the coupling between operator splitting techniques and a time
parallelization scheme, the parareal algorithm,
as a numerical
strategy for the simulation of reaction-diffusion equations modelling multi-scale reaction waves.
This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum
of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in
the reactive...
A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson
equations, and tested in the simplest case of one spatial dimension. The plasma
distribution function is discretized using tracer particles, and the charge distribution
is reconstructed using wavelet-based density estimation. The latter consists in projecting
the Delta distributions corresponding to the particles onto a finite dimensional linear
space spanned by...
In this paper, we study a postprocessing procedure for improving
accuracy of the finite volume element approximations of semilinear
parabolic problems. The procedure amounts to solve a source problem
on a coarser grid and then solve a linear elliptic problem on a
finer grid after the time evolution is finished. We derive error
estimates in the L2 and H1 norms for the standard finite
volume element scheme and an improved error estimate in the H1
norm. Numerical results demonstrate the accuracy...