The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state spaces. Application of these Markov chain results leads to straightforward proofs of ergodicity for a variety of SDEs, in particular for problems with degenerate noise and for problems with locally Lip...

The DC analysis and transient analysis parts of the general electrical circuit analysis program ESACAP are parallelized to run on the Intel iPSC. Most of the program runs unchanged on the cube manager. Only the solution of the systems of nonlinear algebraic equations is parallelized to run on the hypercube parallel computer. The nonlinear equations arise either from the DC problem or from the d...

A morphological multiscale method in 3D image and 3D image sequence processing is discussed which identifies edges on level sets and the motion of features in time. Based on these indicator evaluation the image data is processed applying nonlinear diffusion and the theory of geometric evolution problems. The aim is to smooth level sets of a 3D image while simultaneously preserving geometric fea...

We consider a Fermi pencil beam model in two space dimensions (x; y), where x is aligned with the beam's penetration direction and y together with the scaled angular variable z, correspond to a bounded symmetric , transversal cross section. We study some fully discrete numerical schemes using the standard Galerkin and streamline diiusion nite element methods for discretization of the transversa...

A new formulation, a gauge formulation of the incompressible Navier-Stokes equations in terms of an auxiliary field a and a gauge variable φ, u = a +∇φ, was proposed recently by E and Liu. This paper provides a theoretical analysis of their formulation and verifies the computational advantages. We discuss the implicit gauge method, which uses backward Euler or Crank-Nicolson in time discretizat...

We consider a fully discrete approximation of the H gradient flow of an energy integral where the energy density is given by the sum of a nonnegative multi-well potential term and a bending energy term. The spatial discretization is based on a Fourier spectral method, which is combined with an implicit Euler time discretization. The numerical method is shown to be stable and to exhibit optimal ...

We consider European double barrier basket call options on two underlyings with an upper and a lower knock-out barrier featuring a finite number of cash settlements at prespecified values of the underlyings between the strike and the upper barrier. The bilaterally constrained cash settlements are considered as controls that have to be chosen such that the Delta of the option is as close as poss...

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoi...

Abstract Positive dynamical or control systems have all their variables nonnegative. Euler discretization transforms a continuous-time system into on discrete time scale. Some structural properties of the may be preserved by discretization, while other lost. Four fundamental positive are studied in context discretization: positivity, stability, reachability and observability. Both linear nonlin...

A new formulation, a gauge formulation of the incompressible Navier-Stokes equations in terms of an auxiliary eld a and a gauge variable , u = a + r, was proposed recently by E and Liu. This paper provides a theoretical analysis of their formulation and veriies the computational advantages. We discuss the implicit gauge method, which uses backward Euler or Crank-Nicolson in time discretization....