Numerical approximation of density dependent diffusion in age-structured population dynamics

summary:We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result

Optimized Schwarz Methods for Maxwell equations

Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, and it was observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for which overlap is essential for convergence. Over the last decade, optimized Schwarz methods have been developed for elliptic partial differential equations. These methods use more effective transmission conditions between subdomains, and are also convergent without overlap for elliptic problems. We show here why the classical Schwarz method applied to the hyperbolic problem converges without overlap for Maxwell's equations. The reason is that the method is equivalent to a simple optimized Schwarz method for an equivalent elliptic problem. Using this link, we show how to develop more efficient Schwarz methods than the classical ones for the Maxwell's equations. We illustrate our findings with numerical results

Convergence Analysis of a Domain Decomposition FEM Approximation of the Isentropic Euler Equation

We analyze an interation-by-subdomain algorithm of Dirichlet\Dirichlet type for the isentropic Euler equation. Focusing on subsonic flows, which are the ones showing the most interesting features in a domain decomposition framework. The main attention is paid to the spatial decomposition, and the problem is advanced in time by means of a semi-implicit Euler scheme. We enforce the continuity on the interface of the inviscid flux, and, in the one-dimentional case, we prove convergence of the algorithm in characteristic variables for both the semi-discrete problem and the fully discrete one, where the equation is discretized in space via Streamline Diffusion Finite Elements. In both cases, the interface mapping is showed to be a contraction: in the semi discrete case, for any choice of the time step Dt, with constant of order e (-c/Dt) (c>0), in the fully discrete case, provided the entries of the stabilizing matrix are sufficiently small. Finally, some error estimates of energy type are given

Systematic Characterization of High-Power Short-Duration Ablation: Insight From an Advanced Virtual Model

High-power short-duration (HPSD) recently emerged as a new approach to radiofrequency (RF) catheter ablation. However, basic and clinical data supporting its effectiveness and safety is still scarc

Optimized Schwarz methods for the Stokes-Darcy coupling

This paper studies Optimized Schwarz methods for the Stokes-Darcy problem. Robin transmission conditions are introduced and the coupled problem is reduced to a suitable interface system that can be solved using Krylov methods. Practical strategies to compute optimal Robin coefficients are proposed which take into account both the physical parameters of the problem and the mesh size. Numerical results show the effectiveness of our approach

Large scale simulation of synthetic markets

High-frequency trading has been experiencing an increase of interest both for practical purposes within financial institutions and within academic research; recently, the UK Government Office for Science reviewed the state of the art and gave an outlook analysis. Therefore, models for tick-by-tick financial time series are becoming more and more important. Together with high-frequency trading comes the need for fast simulations of full synthetic markets for several purposes including scenario analyses for risk evaluation. These simulations are very suitable to be run on massively parallel architectures. Aside more traditional large-scale parallel computers, high-end personal computers equipped with several multi-core CPUs and general-purpose GPU programming are gaining importance as cheap and easily available alternatives. A further option are FPGAs. In all cases, development can be done in a unified framework with standard C or C++ code and calls to appropriate libraries like MPI (for CPUs) or CUDA for (GPGPUs). Here we present such a prototype simulation of a synthetic regulated equity market. The basic ingredients to build a synthetic share are two sequences of random variables, one for the inter-trade durations and one for the tick-by-tick logarithmic returns. Our extensive simulations are based on several distributional choices for the above random variables, including Mittag-Leffler distributed inter-trade durations and alpha-stable tick-by-tick logarithmic returns

Is minimizing the convergence rate a good choice for efficient Optimized Schwarz preconditioning in heterogeneous coupling? The Stokes-Darcy case

Optimized Schwarz Methods (OSM) are domain decomposition techniques based on Robin-type interface condition that have became increasingly popular in the last two decades. Ensuring convergence also on non-overlapping decompositions, OSM are naturally advocated for the heterogeneous coupling of multiphysics problems. Classical approaches optimize the coefficients in the Robin condition by minimizing the effective convergence rate of the resulting iterative algorithm. However, when OSM are used as preconditioners for Krylov solvers of the resulting interface problem, such parameter optimization does not necessarily guarantee the fastest convergence. This drawback is already known for homogeneous decomposition, but in the case of heterogeneous decomposition, the poor performance of the classical optimization approach becomes utterly evident. In this paper, we highlight this drawback for the Stokes/Darcy problem and we propose a more effective alternative optimization procedure