Enabling Radiative Transfer on AMR grids in CRASH

We introduce CRASH-AMR, a new version of the cosmological Radiative Transfer (RT) code CRASH, enabled to use refined grids. This new feature allows us to attain higher resolution in our RT simulations and thus to describe more accurately ionisation and temperature patterns in high density regions. We have tested CRASH-AMR by simulating the evolution of an ionised region produced by a single source embedded in gas at constant density, as well as by a more realistic configuration of multiple sources in an inhomogeneous density field. While we find an excellent agreement with the previous version of CRASH when the AMR feature is disabled, showing that no numerical artifact has been introduced in CRASH-AMR, when additional refinement levels are used the code can simulate more accurately the physics of ionised gas in high density regions. This result has been attained at no computational loss, as RT simulations on AMR grids with maximum resolution equivalent to that of a uniform cartesian grid can be run with a gain of up to 60% in computational time.Comment: 19 pages, 17 figures. MNRAS, in pres

High-Dimensional Stochastic Design Optimization by Adaptive-Sparse Polynomial Dimensional Decomposition

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic response for statistical moment and reliability analyses; a novel integration of the adaptive-sparse PDD approximation and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and standard gradient-based optimization algorithms. New analytical formulae are presented for the design sensitivities that are simultaneously determined along with the moments or the failure probability. Numerical results stemming from mathematical functions indicate that the new method provides more computationally efficient design solutions than the existing methods. Finally, stochastic shape optimization of a jet engine bracket with 79 variables was performed, demonstrating the power of the new method to tackle practical engineering problems.Comment: 18 pages, 2 figures, to appear in Sparse Grids and Applications--Stuttgart 2014, Lecture Notes in Computational Science and Engineering 109, edited by J. Garcke and D. Pfl\"{u}ger, Springer International Publishing, 201

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

ELPA: A parallel solver for the generalized eigenvalue problem

For symmetric (hermitian) (dense or banded) matrices the computation of eigenvalues and eigenvectors Ax = λBx is an important task, e.g. in electronic structure calculations. If a larger number of eigenvectors are needed, often direct solvers are applied. On parallel architectures the ELPA implementation has proven to be very efficient, also compared to other parallel solvers like EigenExa or MAGMA. The main improvement that allows better parallel efficiency in ELPA is the two-step transformation of dense to band to tridiagonal form. This was the achievement of the ELPA project. The continuation of this project has been targeting at additional improvements like allowing monitoring and autotuning of the ELPA code, optimizing the code for different architectures, developing curtailed algorithms for banded A and B, and applying the improved code to solve typical examples in electronic structure calculations. In this paper we will present the outcome of this project

The long-term consequences of hybridization between the two Daphnia species, D. galeata and D. dentifera, in mature habitats

<p>Abstract</p> <p>Background</p> <p>Ecological specializations such as antipredator defense can reinforce morphological and distributional divergence within hybridizing species. Two hybridizing species of <it>Daphnia </it>(<it>D. galeata </it>and <it>D. dentifera</it>) are distributed in both Japan and North America; however, these populations have a longer history in Japan than in North America due to the differing impact of the last glaciation on these two regions. We tested the hypothesis that this longer coexistence in Japan would lead to extensive genetic admixture in nuclear and mitochondrial DNA whilst the distinct morphological traits and distributional patterns would be maintained.</p> <p>Results</p> <p>The high level of correspondence among morphological traits, distribution, and mitochondrial and nuclear DNA types for the specimens with <it>D. dentifera </it>mtDNA indicated that the species distinction has been maintained. However, a discordance between mtDNA and nuclear ITS-1 types was observed for most specimens that had <it>D. galeata </it>mtDNA, consistent with the pattern seen between the two species in North America. This observation suggests nuclear introgression from <it>D. dentifera </it>into <it>D. galeata </it>without mitochondrial introgression.</p> <p>Conclusions</p> <p>The separation of morphological traits and distribution ranges of the two hybridizing species in Japan, as well as in North America, has been maintained, despite large differences in climatic and geographical histories of these two regions. Variations in environmental factors, such as predation pressure, might affect maintenance of the distribution, although the further studies are needed to confirm this.</p