Preconditioner for a scattering solver based on the intrusive stochastic Galerkin method accelerated with MLFMM

We present a preconditioner for an intrusive stochastic Galerkin method (SGM) based scattering solver that also leverages the multilevel fast multipole method (MLFMM). The proposed preconditioner is essential in developing a general and intrusive SGM method. Simulation results are obtained for a canonical scattering structure with perfect electrically conducting strips with statistically varying geometry. Results are reported for the number of iterations, with and without using a preconditioner, and for the time required to setup the preconditioner

Perfect and imperfect simulations in stochastic geometry

This thesis presents new developments and applications of simulation methods in stochastic geometry. Simulation is a useful tool for the statistical analysis of spatial point patterns. We use simulation to investigate the power of tests based on the J-function, a new measure of spatial interaction in point patterns. The power of tests based on J is compared to the power of tests based on alternative measures of spatial interaction. Many models in stochastic geometry can only be sampled using Markov chain Monte Carlo methods. We present and extend a new generation of Markov chain Monte Carlo methods, the perfect simulation algorithms. In contrast to conventional Markov chain Monte Carlo methods perfect simulation methods are able to check whether the sampled Markov chain has reached equilibrium yet, thus ensuring that the exact equilibrium distribution is sampled. There are two types of perfect simulation algorithms. Coupling from the Past and Fill’s interruptible algorithm. We present Coupling from the Past in the most general form available and provide a classification of Coupling from the Past algorithms. Coupling from the Past is then extended to produce exact samples of a Boolean model which is conditioned to cover a set of locations with grains. Finally we discuss Fill’s interruptible algorithm and show how to extend the original algorithm to continuous distributions by applying it to a point process example

Limits on the Capacity of In-Band Full Duplex Communication in Uplink Cellular Networks

Simultaneous co-channel transmission and reception, denoted as in-band full duplex (FD) communication, has been promoted as an attractive solution to improve the spectral efficiency of cellular networks. However, in addition to the self-interference problem, cross-mode interference (i.e., between uplink and downlink) imposes a major obstacle for the deployment of FD communication in cellular networks. More specifically, the downlink to uplink interference represents the performance bottleneck for FD operation due to the uplink limited transmission power and venerable operation when compared to the downlink counterpart. While the positive impact of FD communication to the downlink performance has been proved in the literature, its effect on the uplink transmission has been neglected. This paper focuses on the effect of downlink interference on the uplink transmission in FD cellular networks in order to see whether FD communication is beneficial for the uplink transmission or not, and if yes for which type of network. To quantify the expected performance gains, we derive a closed form expression of the maximum achievable uplink capacity in FD cellular networks. In contrast to the downlink capacity which always improves with FD communication, our results show that the uplink performance may improve or degrade depending on the associated network parameters. Particularly, we show that the intensity of base stations (BSs) has a more prominent effect on the uplink performance than their transmission power

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code.Comment: 9 pages, 5 figure