A robust time-space formulation for large-scale scalar wave problems using exponential basis functions

2018 ◽  
Vol 114 (7) ◽  
pp. 719-748 ◽  
Author(s):  
B. Movahedian ◽  
B. Boroomand ◽  
S. Mansouri
Keyword(s):  
Large Scale ◽  
Basis Functions ◽  
Scalar Wave ◽  
Exponential Basis ◽  
Time Space ◽  
Space Formulation ◽  
Wave Problems

Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Large Scale ◽  
Boundary Integral ◽  
Practical Significance ◽  
Fast Multipole ◽  
Tree Structures ◽  
Wave Problems ◽  
Element Method

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

Solving PDEs with radial basis functions

Acta Numerica ◽  
2015 ◽  
Vol 24 ◽  
pp. 215-258 ◽  
Author(s):  
Bengt Fornberg ◽  
Natasha Flyer
Keyword(s):  
Radial Basis Functions ◽  
Finite Differences ◽  
Large Scale ◽  
Numerical Approach ◽  
Basis Functions ◽  
Integration Time ◽  
Small Scale ◽  
Major Step ◽  
Mesh Free ◽  
Radial Basis

Finite differences provided the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods. During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE ‘toy problems’ to becoming a major contender also for very large simulations on advanced distributed memory computer systems. Being entirely mesh-free, RBF-FD discretizations are also particularly easy to implement, even when local refinements are needed. This article gives some background to this development, and highlights some recent results.

Time–Space Characteristics of Diurnal Rainfall over Borneo and Surrounding Oceans as Observed by TRMM-PR

2006 ◽  
Vol 19 (7) ◽  
pp. 1238-1260 ◽  
Author(s):  
Hiroki Ichikawa ◽  
Tetsuzo Yasunari
Keyword(s):  
Diurnal Cycle ◽  
Large Scale ◽  
Intraseasonal Variability ◽  
Phase Speed ◽  
Tropical Rainfall Measuring Mission ◽  
Heavy Precipitation ◽  
Circulation Pattern ◽  
Leeward Side ◽  
Convective Rainfall ◽  
Time Space

Abstract Five years of Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) data were used to investigate the time and space characteristics of the diurnal cycle of rainfall over and around Borneo, an island in the Maritime Continent. The diurnal cycle shows a systematic modulation that is associated with intraseasonal variability in the large-scale circulation pattern, with regimes associated with low-level easterlies or westerlies over the island. The lower-tropospheric westerly (easterly) components correspond to periods of active (inactive) convection over the island that are associated with the passage of intraseasonal atmospheric disturbances related to the Madden–Julian oscillation. A striking feature is that rainfall activity propagates to the leeward side of the island between midnight and morning. The inferred phase speed of the propagation is about 3 m s−1 in the easterly regime and 7 m s−1 in the westerly regime. Propagation occurs over the entire island, causing a leeward enhancement of rainfall. The vertical structure of the developed convection/rainfall system differs remarkably between the two regimes. In the easterly regime, stratiform rains are widespread over the island at midnight, whereas in the westerly regime, local convective rainfall dominates. Over offshore regions, convective rainfall initially dominates then gradually decreases in both regimes, while the storms develop into deeper convective systems in the easterly regime. Aside from leeward rainfall propagation, shallow storms develop over the South China Sea region during the westerly regime, resulting in heavy precipitation from midnight through morning.

Variations in Pathogenicity of Three Different Forms of Rhizoctonia Inoculum and Assessment of Cultivar Resistance of Sugar Beet

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Haque ME ◽  
◽  
Parvin MS ◽  
Keyword(s):  
Seed Germination ◽  
Sugar Beet ◽  
Root Rot ◽  
Large Scale ◽  
Culture Media ◽  
Damping Off ◽  
Require Time ◽  
Time Space ◽  
The Usa

Rhizoctonia solani causes pre-emergence and post-emergence damping-off, as well as crown and root rot of sugar beet (Beta vulgaris L.), which significantly affects the yield returns in the USA and Europe. The pathogen overwinters as sclerotia or melanized mycelium. Traditionally, the resistance of cultivars to R. solani is evaluated by scoring disease reactions at the crowns and roots of older seedlings, thus resistance is not evaluated during seed germination. Moreover, earlier studies evaluated cultivars resistance to R. solani using colonized whole barley or wheat grains which, unlike sclerotia, are artificial inocula of the pathogen that require time, space and technical know-how to produce. Moreover, colonized grains are prone to contamination with other pathogens, consumed by rodents/birds while applied in the field, and are often uneconomic. Considering those limitations, a study was undertaken (1) to develop in vitro methods to generate large-scale sclerotia, (2) to compare pathogenic potentials of sclerotia, mycelia, and colonized barley grains for optimization of dampingoff assays, and (3) to evaluate Rhizoctonia resistance of selected commercial cultivars during the seed germination phase. Comparing six different culture media, we found that R. solani had the highest radial growth (8.9 ± 0.04, cm³) at 8-days and the maximum number of sclerotia produced (203 ± 4.6) at 28-days in CV8 medium. We demonstrated significant differences in pathogenicity of the three different forms of R. solani inocula and susceptibility of cultivars to preand post-emergence damping-off. The highest pre-emergence damping-off and root rot were observed with sclerotia, and the highest post-emergence dampingoff was recorded with both sclerotial and colonized barley inocula. In addition, varietal differences in susceptibility to pre- and post-emergence damping-off were noted. The highest pre-emergence damping-off was recorded on cv Crystal 101RR and lowest in Maribo MA 504. The highest post-emergence damping-off was recorded on BTS 8500 and the lowest in Crystal 467. The maximum mean root rot was observed in BTS 8500, BTS 8606, and Crystal 101R. Our studies demonstrated that sclerotia serve as efficient natural inocula, reemphasized that host-pathogen interactions differ at the early vs. late stages of sugar beet growth, and highlighted the need to reevaluate commercial sugar beet cultivars for resistance at the seed germination stage.

Empirical Studies on the Functional Complexity of Software in Large-Scale Software Systems

2011 ◽  
Vol 3 (3) ◽  
pp. 23-42 ◽  
Author(s):  
Yingxu Wang ◽  
Vincent Chiew
Keyword(s):  
Cognitive Complexity ◽  
Large Scale ◽  
Complexity Analysis ◽  
Software Systems ◽  
Development Effort ◽  
Analysis Tool ◽  
Software System ◽  
Time Space ◽  
Functional Complexity ◽  
Scope Problem

Functional complexity is one of the most fundamental properties of software because almost all other software attributes and properties such as functional size, development effort, costs, quality, and project duration are highly dependent on it. The functional complexity of software is a macro-scope problem concerning the semantic properties of software and human cognitive complexity towards a given software system; while the computational complexity is a micro-scope problem concerning algorithmic analyses towards machine throughput and time/space efficiency. This paper presents an empirical study on the functional complexity of software known as cognitive complexity based on large-scale samples using a Software Cognitive Complexity Analysis Tool (SCCAT). Empirical data are obtained with SCCAT on 7,531 programs and five formally specified software systems. The theoretical foundation of software functional complexity is introduced and the metric of software cognitive complexity is formally modeled. The functional complexities of a large-scale software system and the air traffic control systems (ATCS) are rigorously analyzed. A novel approach to represent software functional complexities and their distributions in software systems is developed. The nature of functional complexity of software in software engineering is rigorously explained. The relationship between the symbolic and functional complexities of software is quantitatively analyzed.

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