Efficient Generating And Processing Of Large-Scale Unstructured Meshes

Unstructured meshes are used in a variety of disciplines to represent simulations and experimental data. Scientists who want to increase accuracy of simulations by increasing resolution must also increase the size of the resulting dataset. However, generating and processing a extremely large unstructured meshes remains a barrier. Researchers have published many parallel Delaunay triangulation (DT) algorithms, often focusing on partitioning the initial mesh domain, so that each rectangular partition can be triangulated in parallel. However, the comproblems for this method is how to merge all triangulated partitions into a single domain-wide mesh or the significant cost for communication the sub-region borders. We devised a novel algorithm --Triangulation of Independent Partitions in Parallel (TIPP) to deal with very large DT problems without requiring inter-processor communication while still guaranteeing the Delaunay criteria. The core of the algorithm is to find a set of independent} partitions such that the circumcircles of triangles in one partition do not enclose any vertex in other partitions. For this reason, this set of independent partitions can be triangulated in parallel without affecting each other. The results of mesh generation is the large unstructured meshes including vertex index and vertex coordinate files which introduce a new challenge \-- locality. Partitioning unstructured meshes to improve locality is a key part of our own approach. Elements that were widely scattered in the original dataset are grouped together, speeding data access. For further improve unstructured mesh partitioning, we also described our new approach. Direct Load which mitigates the challenges of unstructured meshes by maximizing the proportion of useful data retrieved during each read from disk, which in turn reduces the total number of read operations, boosting performance

Electronic scan weather radar: scan strategy and signal processing for volume targets

2013 Fall.Includes bibliographical references.Following the success of the WSR-88D network, considerable effort has been directed toward searching for options for the next generation of weather radar technology. With its superior capability for rapidly scanning the atmosphere, electronically scanned phased array radar (PAR) is a potential candidate. A network of such radars has been recommended for consideration by the National Academies Committee on Weather Radar Technology beyond NEXRAD. While conventional weather radar uses a rotating parabolic antenna to form and direct the beam, a phased array radar superimposes outputs from an array of many similar radiating elements to yield a beam that is scanned electronically. An adaptive scan strategy and advanced signal designs and processing concepts are developed in this work to use PAR effectively for weather observation. An adaptive scan strategy for weather targets is developed based on the space-time variability of the storm under observation. Quickly evolving regions are scanned more often and spatial sampling resolution is matched to spatial scale. A model that includes the interaction between space and time is used to extract spatial and temporal scales of the medium and to define scanning regions. The temporal scale constrains the radar revisit time while the measurement accuracy controls the dwell time. These conditions are employed in a task scheduler that works on a ray-by-ray basis and is designed to balance task priority and radar resources. The scheduler algorithm also includes an optimization procedure for minimizing radar scan time. In this research, a signal model for polarimetric phased array weather radar (PAWR) is presented and analyzed. The electronic scan mechanism creates a complex coupling of horizontal and vertical polarizations that produce the bias in the polarimetric variables retrieval. Methods for bias correction for simultaneous and alternating transmission modes are proposed. It is shown that the bias can be effectively removed; however, data quality degradation occurs at far off boresight directions. The effective range for the bias correction methods is suggested by using radar simulation. The pulsing scheme used in PAWR requires a new ground clutter filtering method. The filter is designed to work with a signal covariance matrix in the time domain. The matrix size is set to match the data block size. The filter's design helps overcome limitations of spectral filtering methods and make efficient use of reducing ground clutter width in PAWR. Therefore, it works on modes with few samples. Additionally, the filter can be directly extended for staggered PRT waveforms. Filter implementation for polarimetric retrieval is also successfully developed and tested for simultaneous and alternating staggered PRT. The performance of these methods is discussed in detail. It is important to achieve high sensitivity for PAWR. The use of low-power solid state transmitters to keep costs down requires pulse compression technique. Wide-band pulse compression filters will partly reduce the system sensitivity performance. A system for sensitivity enhancement (SES) for pulse compression weather radar is developed to mitigate this issue. SES uses a dual-waveform transmission scheme and an adaptive pulse compression filter that is based on the self-consistency between signals of the two waveforms. Using SES, the system sensitivity can be improved by 8 to 10 dB

Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure

We prove the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents and elastic labor supply. The method of proof relies on exploiting the existence of Lagrange multipliers in infinite dimensional spaces and the link between Pareto-optima and competitive equilibria.Optimal growth model, Lagrange multipliers, single-sector growth model, competitive equilibrium, elastic labor supply.

Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor

The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.Single-sector growth model, heterogeneous agents, elastic labor supply, supermodularity

Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor

The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths.Single-sector growth model, heterogeneous agents, elastic labor supply.

Existence of competitive equilibrium in an optimal growth model with heterogeneous agents and endogenous leisure

This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply and complete assets markets. The method of proof relies on some recent results concerning the existence of Lagrande multipliers in infinite dimensional spaces and their representation as a summable sequence and a direct application of the inward boundary fixed point theorem.Optimal growth model, Lagrange multipliers, competitive equilibrium, individually rational Pareto Optimum, elastic labor supply.

Non-convex Aggregate Technology and Optimal Economic Growth

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state equilibrium toward which the convergence of the optimal paths is monotone and asymptotic. When the discount rate is in some intermediate range, we find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, the optimal paths converge to one single appropriate equilibrium steady state. This state might be a poverty trap with low per capita capital, which acts as the extinction state encountered in earlier studies focused on S-shapes production functions. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range . In the latter case, we give conditions under which the above critical value might not exist, and the economy attains one steady state infinite time, then stays at the other steady state afterward.Non-convex agreggative technology - optimal economic growth - steady state

Nonlinear approximations of functions having mixed smoothness

For multivariate Besov-type classes $U^a_{p,\theta}$ of functions having nonuniform mixed smoothness  a\in\rr^d_+, we obtain the asumptotic order of entropy numbers $\epsilon_n(U^a_{p,\theta},L_q)$ and non-linear widths $\rho_n(U^a_{p,\theta},L_q)$ defined via pseudo-dimension.  We obtain also the asymptotic order of optimal methods of adaptive sampling recovery in $L_q$-norm of functions in $U^a_{p,\theta}$ by sets of a finite capacity which is measured by their cardinality or pseudo-dimension