Use Of Space-filling Curves Research Articles

Memory access optimization for particle operations in computational fluid dynamics-discrete element method simulations

Computational Fluid Dynamics – Discrete Element Method is used to model gas-solid systems in several applications in energy, pharmaceutical and petrochemical industries. Computational performance bottlenecks often limit the problem sizes that can be simulated at industrial scale. The data structures used to store several millions of particles in such large-scale simulations have a large memory footprint that does not fit into the processor cache hierarchies on current high-performance-computing platforms, leading to reduced computational performance. This paper specifically addresses this aspect of memory access bottlenecks in industrial scale simulations. The use of space-filling curves to improve memory access patterns is described and their impact on computational performance is quantified in both shared and distributed memory parallelization paradigms. The Morton space filling curve applied to uniform grids and k-dimensional tree partitions are used to reorder the particle data-structure thus improving spatial and temporal locality in memory. The performance impact of these techniques when applied to two benchmark problems, namely the homogeneous-cooling-system and a fluidized-bed, are presented. These optimization techniques lead to approximately two-fold performance improvement in particle focused operations such as neighbor-list creation and data-exchange, with ∼ 1.5 times overall improvement in a fluidization simulation with 1.27 million particles.

A Fast kNN Algorithm Using Multiple Space-Filling Curves.

The paper considers a time-efficient implementation of the k nearest neighbours (kNN) algorithm. A well-known approach for accelerating the kNN algorithm is to utilise dimensionality reduction methods based on the use of space-filling curves. In this paper, we take this approach further and propose an algorithm that employs multiple space-filling curves and is faster (with comparable quality) compared with the kNN algorithm, which uses kd-trees to determine the nearest neighbours. A specific method for constructing multiple Peano curves is outlined, and statements are given about the preservation of object proximity information in the course of dimensionality reduction. An experimental comparison with known kNN implementations using kd-trees was performed using test and real-life data.

Use of space-filling curves for additive manufacturing of three dimensionally varying graded dielectric structures using fused deposition modeling

In this paper the authors present a novel design tool for realizing dielectric structures with spatially varying electromagnetic properties via additive manufacturing (AM). To create tool paths ideal for AM processes, space-filling curves were utilized. Using fused deposition modeling (FDM), spatially varying structures were printed that produced a spatially varying relative permittivity. A wide range of varying fill fractions were printed and evaluated, demonstrating good agreement between the simulated and measured results. Furthermore, the authors verified that this design tool can be applied to practical structures by designing, printing and testing a gradient index flat lens.

On the similarity analysis of spatial patterns

The evaluation of the spatial similarity of two observed point patterns is an important issue in spatial data quality assessment. In this work we propose a formal procedure that takes advantage of the joint use of space-filling curves and the multinomial model in order to establish a statistical test to compare spatial point patterns. In this mix, the space-filling curves offer a mechanism to order the 2D, 3D or n-D space and the multinomial distribution the statistical approach for testing homogeneity. A simulation method is proposed in order to analyze the applied performance of this idea.

Use of space-filling curves to select sample locations in natural resource monitoring studies

The establishment of several large area monitoring networks over the past few decades has led to increased research into ways to spatially balance sample locations across the landscape. Many of these methods are well documented and have been used in the past with great success. In this paper, we present a method using geographic information systems (GIS) and fractals to create a sampling frame, superimpose a tessellation and draw a sample. We present a case study that illustrates the technique and compares results to those from other methods using data from Voyageurs National Park in Minnesota. Our method compares favorably with results from a popular plot selection method, Generalized Random Tessellation Stratified Design, and offers several additional advantages, including ease of implementation, intuitive appeal, and the ability to maintain spatial balance by adding new plots in the event of an inaccessible plot encountered in the field.

Broad-band and circularly polarized space-filling-based slot antennas

Based on the use of space-filling curves, broad-band and circularly polarized microstrip-fed slot antennas are proposed. Broad-band performance is achieved through merging different downscaled versions of a composition of island-like space-filling slot antennas without increasing the overall antenna size. This technique provides different resonant slot lengths corresponding to a wide range of frequencies. By merging three downscaled versions of a composite second-iteration Moore slot antenna, a broad-band slot antenna is developed. The proposed antenna has a bandwidth (VSWR<2) of 87.6% around 4.5 GHz, which is higher by a factor of 13.5 compared to the square ring slot antenna, and by a factor of 3 compared to the nested square rings slot antenna. The developed slot antenna has a maximum gain of 5 dB and a total area of 3/spl times/3 cm/sup 2/. Furthermore, by introducing asymmetry in the proposed slot antenna, which is implemented by replacing all parallel slots on one side of the structure and all inner slots by a ground plane, circular polarization is achieved. The circularly polarized slot antenna version has a 3-dB axial ratio bandwidth of 22% with VSWR<2. The design and simulation of the proposed slot antennas have been performed using a moment-method-based full-wave electromagnetic simulator. Measurements of fabricated antennas are in good agreement with simulation results.

Data-partitioning using the Hilbert space filling curves: Effect on the speed of convergence of Fuzzy ARTMAP for large database problems

The Fuzzy ARTMAP algorithm has been proven to be one of the premier neural network architectures for classification problems. One of the properties of Fuzzy ARTMAP, which can be both an asset and a liability, is its capacity to produce new nodes (templates) on demand to represent classification categories. This property allows Fuzzy ARTMAP to automatically adapt to the database without having to a priori specify its network size. On the other hand, it has the undesirable side effect that large databases might produce a large network size (node proliferation) that can dramatically slow down the training speed of the algorithm. To address the slow convergence speed of Fuzzy ARTMAP for large database problems, we propose the use of space-filling curves, specifically the Hilbert space-filling curves (HSFC). Hilbert space-filling curves allow us to divide the problem into smaller sub-problems, each focusing on a smaller than the original dataset. For learning each partition of data, a different Fuzzy ARTMAP network is used. Through this divide-and-conquer approach we are avoiding the node proliferation problem, and consequently we speedup Fuzzy ARTMAP's training. Results have been produced for a two-class, 16-dimensional Gaussian data, and on the Forest database, available at the UCI repository. Our results indicate that the Hilbert space-filling curve approach reduces the time that it takes to train Fuzzy ARTMAP without affecting the generalization performance attained by Fuzzy ARTMAP trained on the original large dataset. Given that the resulting smaller datasets that the HSFC approach produces can independently be learned by different Fuzzy ARTMAP networks, we have also implemented and tested a parallel implementation of this approach on a Beowulf cluster of workstations that further speeds up Fuzzy ARTMAP's convergence to a solution for large database problems.

Miniaturized Fractal Rat-Race, Branch-Line, and Coupled-Line Hybrids

In this paper, space-filling curves have been used to realize a family of miniaturized hybrids. The large surface area occupied by a conventional structure has been significantly reduced through the use of space-filling curves having the same electrical characteristics. Several space-filling curves have been studied and implemented in different designs. The second-iteration Moore rat-race coupler occupies only 12.6% of the conventional coupler's area, while the area of the second-iteration Sierpinski branch-line coupler is 24.7% of the conventional case. On the other hand, a nine-section Minkowski coupled-line balun is confined in 60% of the conventional balun's area. However, the effective size reduction depends on the used space-filling curve, compression ratio, and associated coupling between segments. The performance of the proposed space-filling hybrids is as good as that of the corresponding conventional structures, and even better in some cases. The design and simulation of the proposed space-filling hybrids have been performed using a moment-method-based full-wave electromagnetic simulator. Measurements of one fabricated coupler prototype are in good agreement with simulation results.

Use of Space-Filling Curves in Generating a National Rural Sampling Frame for HIV/AIDS Research∗

The classical geographic research problem of regionalization and resource allocation is most commonly tackled by means of location-allocation methods. This paper introduces the spatial-order method as an alternative for creating regions or clusters. The spatial-order method utilizes space-filling curves, also known as Peano curves, to determine the nearness or spatial order of areal units, such as counties. Given a capacity constraint, the areal units are grouped consecutively according to their spatial order values. We applied the method to create clusters of rural counties for a national sampling survey of HIV/AIDS patients in the United States. Using the criteria that each cluster had approximately 50 new AIDS cases in 1991–1993 and that contiguity of areal units was maximized, 226 clusters were created from the 1,853 rural counties or health districts. The rural clusters generated by this method have been adopted as the national rural sampling frame in the HIV Cost and Services Utilization Study (HCSU...

Die Lösung der Schrödinger-Gleichung als eindimensionales Problem. I. Der Formalismus

Abstract In this article a new method for solving the multi-dimensional Schrödinger-equation for electrons and nuclei will be discussed. It is shown by application of integral transformations and by use of space-filling curves how the multi-dimensional Schrödinger-equation can be replaced by an one­ dimensional integral equation. Furthermore the problems of accuracy arising due to the use of this approximative treatment are pointed out. The presented method can be stated without the Born-Oppenheimer approximation and the application of determinants for fitting the wave function is discussed in a new one-dimensional point of view.

An Improvement-Type Layout Algorithm for Single and Multiple-Floor Facilities

In this paper we introduce the use of spacefilling curves in facility layout, and we extend a well-known facility layout algorithm () to facilities with multiple floors. Spacefilling curves make it possible to exchange any two departments and to use more powerful exchange routines than two-way or three-way exchanges. We also further enhance CRAFT by controlling department shapes, and (with multiple floors) by allowing “flexible” departmental area requirements. Although the algorithm we present can be used for any single-floor or multi-floor facility layout problem, its primary target is production facilities. A tailored version of the algorithm was successfully tested and used in a large, multi-floor production facility. The algorithm differs significantly from two previous extensions of to multi-floor facilities.

On the generation and use of space‐filling curves

On the generation and use of space‐filling curves