Hybrid Approximation Hierarchical Boundary Element Methods for Acoustic Problems

2017 ◽  
Vol 25 (03) ◽  
pp. 1750013 ◽  
Author(s):  
Xiujuan Liu ◽  
Haijun Wu ◽  
Weikang Jiang
Keyword(s):  
Boundary Element ◽  
High Efficiency ◽  
Hybrid Methods ◽  
Multipole Expansion ◽  
Boundary Element Methods ◽  
Memory Consumption ◽  
Expansion Theory ◽  
Set Up ◽  
And Storage ◽  
Hybrid Approximation

A multipole expansion approximation boundary element method (MEA BEM) based on the hierarchical matrices (H-matrices) and the multipole expansion theory was proposed previously. Though the MEA BEM can obtain higher accuracy than the adaptive cross-approximation BEM (ACA BEM), it demands more CPU time and memory than the ACA BEM does. To alleviate this problem, in this paper, two hybrid BEMs are developed taking advantage of the high efficiency and low memory consumption property of the ACA BEM and the high accuracy advantage of the MEA BEM. Numerical examples are elaborately set up to compare the accuracy, efficiency and memory consumption of the ACA BEM, MEA BEM and hybrid methods. It is indicated that the hybrid BEMs can reach the same level of accuracy as the ACA BEM and MEA BEM. The efficiency of each hybrid BEM is higher than that of the MEA BEM but lower than that of the ACA BEM. The memory consumptions of the hybrid BEMs are larger than that of the ACA BEM but less than that of the MEA BEM. The algorithm used to approximate the far-field submatrices corresponding to the cells and their nearest interactional cells determines the accuracy, efficiency and memory consumption of the hybrid BEMs. The proposed hybrid BEMs have both operation and storage logarithmic-linear complexity. They are feasible.

Efficient Computations of Fully-Nonlinear Wave Interactions With Floating Structures

2010 ◽  
Author(s):  
Hongmei Yan ◽  
Yuming Liu
Keyword(s):  
Boundary Element ◽  
High Efficiency ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Computational Effort ◽  
Boundary Element Methods ◽  
Computational Method ◽  
Wave Interactions ◽  
Time Step ◽  
Fully Nonlinear

We consider the problem of fully nonlinear three-dimensional wave interactions with floating bodies with or without a forward speed. A highly efficient time-domain computational method is developed in the context of potential flow formulation using the pre-corrected Fast Fourier Transform (PFFT) algorithm based on a high-order boundary element method. The method reduces the computational effort in solving the boundary-value problem at each time step to O(NlnN) from O(N2∼3) of the classical boundary element methods, where N is the total number of unknowns. The high efficiency of this method allows accurate computations of fully-nonlinear hydrodynamic loads, wave runups, and motions of surface vessels and marine structures in rough seas. We apply this method to study the hydrodynamics of floating objects with a focus on the understanding of fully nonlinear effects in the presence of extreme waves and large-amplitude body motions.

A Boundary Element Method Based on the Hierarchical Matrices and Multipole Expansion Theory for Acoustic Problems

2018 ◽  
Vol 15 (03) ◽  
pp. 1850009 ◽  
Author(s):  
Xiujuan Liu ◽  
Haijun Wu ◽  
Weikang Jiang
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Large Scale ◽  
Multipole Expansion ◽  
Hierarchical Matrices ◽  
Low Rank ◽  
Scale Model ◽  
Degenerate Kernel ◽  
Set Up ◽  
Element Method

The coefficient matrices of conventional boundary element method (CBEM) are dense and fully populated. Special techniques such as hierarchical matrices (H-matrices) format are required to extent its ability of handling large-scale problems. Adaptive cross approximation (ACA) algorithm is a widely adopted algorithm to obtain the H-matrices. However, the accuracy of the ACA boundary element method (ACABEM) cannot be adjusted by changing the tolerance [Formula: see text] when it exceeds a certain value. In this paper, the degenerate kernel approximation idea for the low-rank matrices is developed to build a fast BEM for acoustic problems by exploring the multipole expansion of the kernel, which is referred as the multipole expansion H-matrices boundary element method (ME-H-BEM). The newly developed algorithm compresses the far-field submatrices into low rank submatrices with the expansion terms of Green’s function. The obtained H-matrices are applied in conjunction with the generalized minimal residual method (GMRES) to solve acoustic problems. Numerical examples are carefully set up to compare the accuracy, efficiency as well as memory consumption of the CBEM, ACABEM, fast multipole boundary element method (FMBEM) and ME-H-BEM. The results of a pulsating sphere indicate that the ME-H-BEM keeps both storage and operation logarithmic-linear complexity of the H-matrices format as the ACABEM does. Moreover, the ME-H-BEM can achieve better convergence and higher accuracy than the ACABEM. For the analyzed complicated large-scale model, the ME-H-BEM with appropriate number of expansion terms has an advantage in terms of efficiency as compared with the ACABEM. Compared with the FMBEM, the ME-H-BEM is easier to be implemented.

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

scholarly journals Chemical and Biological Molecules Involved in Differentiation, Maturation, and Survival of Dopaminergic Neurons in Health and Parkinson’s Disease: Physiological Aspects and Clinical Implications

Biomedicines ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 754
Author(s):  
Giulia Gaggi ◽  
Andrea Di Credico ◽  
Pascal Izzicupo ◽  
Giovanni Iannetti ◽  
Angela Di Baldassarre ◽  
...  
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Dopaminergic Neurons ◽  
Potential Role ◽  
High Efficiency ◽  
Biological Molecules ◽  
Alternative Approach ◽  
Non Coding Rnas ◽  
Set Up

Parkinson’s disease (PD) is one of the most common neurodegenerative disease characterized by a specific and progressive loss of dopaminergic (DA) neurons and dopamine, causing motor dysfunctions and impaired movements. Unfortunately, available therapies can partially treat the motor symptoms, but they have no effect on non-motor features. In addition, the therapeutic effect reduces gradually, and the prolonged use of drugs leads to a significative increase in the number of adverse events. For these reasons, an alternative approach that allows the replacement or the improved survival of DA neurons is very appealing for the treatment of PD patients and recently the first human clinical trials for DA neurons replacement have been set up. Here, we review the role of chemical and biological molecules that are involved in the development, survival and differentiation of DA neurons. In particular, we review the chemical small molecules used to differentiate different type of stem cells into DA neurons with high efficiency; the role of microRNAs and long non-coding RNAs both in DA neurons development/survival as far as in the pathogenesis of PD; and, finally, we dissect the potential role of exosomes carrying biological molecules as treatment of PD.

scholarly journals Sustainable Ventilation Strategies for a Medium-Sized Space with Regional Effect

2021 ◽  
Vol 13 (9) ◽  
pp. 4651
Author(s):  
Ming-Lun Alan Fong
Keyword(s):  
Life Cycle ◽  
Life Cycle Cost ◽  
Co2 Emission ◽  
High Efficiency ◽  
Regional Climate ◽  
Cost Effective ◽  
Regional Effect ◽  
Climate Conditions ◽  
Ventilation Strategies ◽  
Set Up

The analysis of ventilation strategies is fundamentally affected by regional climate conditions and local cost databases, in terms of energy consumption, CO2 emission and cost-effective analysis. A systematic approach is covered in this paper to estimate a local economic and environmental impact on a medium-sized space located in two regions during supply-and-installation and operation phases. Three ventilation strategies, including mixing ventilation (MV), displacement ventilation (DV) and stratum ventilation (SV) were applied to medium-sized air-conditioned space with this approach. The trend of the results for three ventilation systems in the life cycle assessment (LCA) and life cycle cost (LCC) analysis is SV < DV < MV. The result of CO2 emission and regional LCC shows that SV is the lowest one in both regional studies. In comparison with the Hong Kong Special Administrative Region (HKSAR) during 20 Service years, the case analysis demonstrates that the percentage differences in LCC analysis of MV, DV & SV in Guangdong are less than 20.5%, 19.4% and 18.82% respectively. Their CO2 emission of MV, DV and SV in Guangdong are more than HKSAR in 10.69%, 11.22% and 12.05%, respectively. The present study could provide information about regional effects in the LCA and LCC analysis of three ventilation strategies emissions, and thereby help set up models for decision-making on high efficiency and cost-effective ventilation strategy plans.

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