We look at adaptive time integration in the context of discontinuous Galerkin methods for the three dimensional unsteady compressible Navier-Stokes equations. Several explicit and implicit schemes will be compared. Philipp Birken, Gregor Gassner, Mark Haas and Claus-Dieter Munz

The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations – the rotational vector, the Argyris tangential vector and t...

The longitudinal instability in the long-wavelength range is observed experimentally at GSI. Two different simulation schemes (Particle-In-Cell and direct integration on a grid) are employed to understand the long time evolution of the instability.

We study the design of a general, fully explicit numerical method for simulating kinetic equations with an extended BGK collision model allowing for multiple relaxation times. In that case, the problem is stiff and we show that its spectrum consists of multiple separated eigenvalue clusters. Projective integration methods are explicit integration schemes that first take a few small (inner) step...

We propose a new class of the exponential propagation iterative methods of RungeKutta-type (EPIRK). The EPIRK schemes are exponential integrators that can be competitive with explicit and implicit methods for integration of large stiff systems of ODEs. Introducing the new, more general then previously proposed, ansatz for EPIRK schemes allows for more flexibility in deriving computationally eff...

This paper introduces a new classifier, that is based on fuzzy-integration schemes controlled by a genetic optimisation procedure. Two different types of integration are proposed here, and are validated by experiments on real data sets of biological cells. The performance of our classifier is tested against a feed-forward neural network and a Support Vector Machine. Results show the good perfor...

In this article we show in detail the derivation of an integration scheme for the dissipative particle dynamic model (DPD) using the stochastic Trotter formula [1]. We explain some subtleties due to the stochastic character of the equations and exploit analyticity in some interesting parts of the dynamics. The DPD-Trotter integrator demonstrates the inexistence of spurious spatial correlations ...

The implicit equations of a symplectic-energymomentum integrator are not easily solved, especially for small time steps. An inefficient, nested iteration scheme has typically been used to solve these equations. We describe new, more efficient, iteration schemes which avoid nested iterations. We present simulation results comparing five different secondorder, integration methods for two differen...

This paper introduces multi-terminal decision diagrams (MTDDs), a generalisation of MTBDDs [15], as a data structure for representing real-valued functions whose arguments are boolean or real variables. These new structures are suitable for numerical integration using quadrature formulas, like trapezoidal, Simpson and Romberg integration schemes. As an application example, we show how MTDDs can...

This paper applies the global radial basis functions as a spatial collocation scheme for solving the Options Pricing model. Diierent numerical time integration schemes are employed for the time derivative of the model. It is shown that the major numerical error is from the time integration instead of the spatial approximation by comparing with the analytical solution. Since the basis functions ...