We have adapted a simple method of numerical integration to predict the equilibrium state of a population of components undergoing reversible association according to the Law of Mass Action. Its particular application is to populations of protein molecules in aqueous solution. The method is based on Euler integration but employs an adaptive step size: the time increment being reduced if it woul...

In this thesis, which consists of four papers, approximation of optimal control problems is studied. In Paper I the Symplectic Pontryagin method for approximation of optimally controlled ordinary differential equations is presented. The method consists of a Symplectic Euler time stepping scheme for a Hamiltonian system with a regularized Hamiltonian. Under some assumptions it is shown that the ...

The purpose of this paper is to present techniques to solve higher-order finite element discretizations on massively parallel architectures. Implicit schemes are considered as a means of achieving mesh independent convergence rates for both time dependent problems and steady state solutions obtained through pseudo-transient continuation. Domain decomposition preconditioners are presented for th...

The purpose of this article is to put forward the claim that Hurwitz’s paper “Über die Erzeugung der Invarianten durch Integration.” [Gött. Nachrichten (1897), 71-90] should be regarded as the origin of random matrix theory in mathematics. Here Hurwitz introduced and developed the notion of an invariant measure for the matrix groups SO(N) and U(N). He also specified a calculus from which the ex...

The reconnection of a trefoil vortex knot is examined numerically to determine how its helicity and two of its vorticity norms behave. During an initial phase, the helicity is remarkably preserved, as reported in recent experiments (Scheeler et al. 2014a). In addition, the enstrophy (Z) has self-similar growth where all √ νZ(t) converge at a viscosity-independent time tx. This effect requires t...