Invasive Computing in HPC with X10

High performance computing with thousands of cores relies on distributed memory due to memory consistency reasons. The resource management on such systems usually relies on static assignment of resources at the start of each application. Such a static scheduling is incapable of starting applications with required resources being used by others since a reduction of resources assigned to applications without stopping them is not possible. This lack of dynamic adaptive scheduling leads to idling resources until the remaining amount of requested resources gets available. Additionally, applications with changing resource requirements lead to idling or less efficiently used resources. The invasive computing paradigm suggests dynamic resource scheduling and applications able to dynamically adapt to changing resource requirements. As a case study, we developed an invasive resource manager as well as a multigrid with dynamically changing resource demands. Such a multigrid has changing scalability behavior during its execution and requires data migration upon reallocation due to distributed memory systems. To counteract the additional complexity introduced by the additional interfaces, e. g. for data migration, we use the X10 programming language for improved programmability. Our results show improved application throughput and the dynamic adaptivity. In addition, we show our extension for the distributed arrays of X10 to support data migrationThis work was supported by the German Research Foundation (DFG) as part of the Transregional Collaborative Research Centre “Invasive Computing” (SFB/TR 89)

Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings

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

Sparse Pseudospectral Approximation Method

Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two or three dimensions, a sparse grid numerical integration rule offers accuracy with a smaller node set compared to tensor product approximation. However, when using a sparse rule to approximately integrate these coefficients, one often finds unacceptable errors in the coefficients associated with higher degree polynomials. By reexamining Smolyak's algorithm and exploiting the connections between interpolation and projection in tensor product spaces, we construct a sparse pseudospectral approximation method that accurately reproduces the coefficients of basis functions that naturally correspond to the sparse grid integration rule. The compelling numerical results show that this is the proper way to use sparse grid integration rules for pseudospectral approximation

Modelling social identification and helping in evacuation simulation

Social scientists have criticised computer models of pedestrian streams for their treatment of psychological crowds as mere aggregations of individuals. Indeed most models for evacuation dynamics use analogies from physics where pedestrians are considered as particles. Although this ensures that the results of the simulation match important physical phenomena, such as the deceleration of the crowd with increasing density, social phenomena such as group processes are ignored. In particular, people in a crowd have social identities and share those social identities with the others in the crowd. The process of self categorisation determines norms within the crowd and influences how people will behave in evacuation situations. We formulate the application of social identity in pedestrian simulation algorithmically. The goal is to examine whether it is possible to carry over the psychological model to computer models of pedestrian motion so that simulation results correspond to observations from crowd psychology. That is, we quantify and formalise empirical research on and verbal descriptions of the effect of group identity on behaviour. We use uncertainty quantification to analyse the model’s behaviour when we vary crucial model parameters. In this first approach we restrict ourselves to a specific scenario that was thoroughly investigated by crowd psychologists and where some quantitative data is available: the bombing and subsequent evacuation of a London underground tube carriage on July 7th 2005

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