There is a large variety of Local Linearization (LL) schemes for the numerical integration of initial value problems, which differ with respect to the algorithm that is used in the numerical implementation of the Local Linear Discretization. However, in contrast with the LL Discretization, the order of convergence of the LL schemes have not been studied. In this paper, a general theorem about t...

We present a monolithic approach to large-deformation fluid-structure interaction (FSI) problems that allows for choosing fully implicit, single-step and single-stage time integration schemes in the structure and fluid field independently, and hence is tailored to the needs of the individual field. The independent choice of time integration schemes is achieved by temporal consistent interpolati...

Added-mass instability is known to be an important issue in the partitioned approach for fluid-structure interaction (FSI) solvers. Despite the implementation of the implicit approach, convergence of solution can be difficult to achieve. Relaxation may be applied to improve this implicitness of the partitioned algorithm, but this commonly leads to a significant increase in computational time. T...

This is a PhD project proposal for Morten Dahlby, the advisor is Brynjulf Owren. The topic of the project is numerical integration of nonlinear wave models, with special emphasis on structure preserving and geometric integrators. The goal is to study conservative nite di erence schemes, multi-symplectic integrators, exponential integrators and schemes based on Euler's equations. As a part of Wa...

The MRFM device is a powerful setup for manipulating single electron spin in resonance in a magnetic field. However, the real time observation of a resonating spin is still an issue because of the very low SNR of the output signal. This paper investigates the usability and the efficiency of sequential detection schemes (the Sequential Probability Ratio Test) to decrease the required integration...

We describe the implementation of some parallelization schemes for a relativistic four-component Dirac–Kohn–Sham program (BERTHA). The coulomb matrix construction has been parallelized by block-distributing the two-electron integral calculation, while for the exchange-correlation the numerical integration grid was distributed. Both schemes yield excellent performance results in terms of speed-u...

The construction of symplectic numerical schemes for stochastic Hamiltonian systems is studied. An approach based on generating functions method is proposed to generate the stochastic symplectic integration of any desired order. In general the proposed symplectic schemes are fully implicit, and they become computationally expensive for mean square orders greater than two. However, for stochasti...

Two new finite difference schemes based on the method of characteristics are presented for convection-diffusion problems. Both of the schemes are of second order in time, and the matrices of the derived systems of linear equations are symmetric. No numerical integration is required for them. The one is of first order in space and the other is of second order. For the former scheme, an optimal e...

This paper develops a formalism for the design of conserving time-integration schemes for Hamiltonian systems with symmetry. The main result is that, through the introduction of a discrete directional derivative, implicit second-order conserving schemes can be constructed for general systems which preserve the Hamiltonian along with a certain class of other first integrals arising from affine s...

When one solves differential equations, modeling biological or physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. In this work, we introduce explicit finite difference schemes based on the nonstandard discretization method to a...