scholarly journals Comparison of two wave element methods for the Helmholtz problem

2009 ◽  
Vol 25 (1) ◽  
pp. 35-52 ◽  
Author(s):  
T. Huttunen ◽  
P. Gamallo ◽  
R. J. Astley
Keyword(s):  
Helmholtz Problem ◽  
Wave Element

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

scholarly journals Design of Wave Glider Optimal Parameters Suitable for the Northwest Pacific Ocean, the North Indian Ocean, and the South China Sea

2021 ◽  
Vol 9 (4) ◽  
pp. 408
Author(s):  
Xi Chen ◽  
Mei Hong ◽  
Shiqi Wu ◽  
Kefeng Liu ◽  
Kefeng Mao
Keyword(s):  
Indian Ocean ◽  
South China Sea ◽  
South China ◽  
North Indian Ocean ◽  
Northwest Pacific ◽  
Northwest Pacific Ocean ◽  
The North ◽  
Wave Element ◽  
Wave Glider ◽  
The Northwest Pacific Ocean

To study the optimal design of Wave Glider parameters in the wave environment of the Northwest Pacific Ocean, the North Indian Ocean, and the South China Sea, the average velocity of a Wave Glider was taken as the evaluation criterion. Wave reanalysis data from ERA5 were used to classify the mean wave height and period into five types by the K-means clustering method. In addition, a dynamic model was used to simulate the influence of umbilical length, airfoil, and maximum limited angle on the velocity of the Wave Glider under the five types of wave element. The force of the wings was simulated using FLUENT as the model input. The simulation results show that (1) 7 m is the most suitable umbilical length; (2) a smaller relative thickness should be selected in perfect conditions; and (3) for the first type of wave element, 15° is the best choice for the maximum limited angle, and 20° is preferred for the second, third, and fourth types, while 25° is preferred for the fifth type.

scholarly journals Green Function on a Quantum Disk for the Helmholtz Problem

2013 ◽  
Vol 124 (4) ◽  
pp. 636-640 ◽  
Author(s):  
B. Benali ◽  
B. Boudjedaa ◽  
M.T. Meftah
Keyword(s):  
Green Function ◽  
Quantum Disk ◽  
Helmholtz Problem

scholarly journals A Semi-Implicit Version of the MPAS-Atmosphere Dynamical Core

2015 ◽  
Vol 143 (9) ◽  
pp. 3838-3855 ◽  
Author(s):  
Steven Sandbach ◽  
John Thuburn ◽  
Danail Vassilev ◽  
Michael G. Duda
Keyword(s):  
Time Integration ◽  
Standard Test ◽  
Newton Iteration ◽  
Atmospheric Modeling ◽  
Implicit Time ◽  
Integration Scheme ◽  
Baroclinic Wave ◽  
Time Step ◽  
Integration Schemes ◽  
Helmholtz Problem

Abstract An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%–20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.

scholarly journals A D-N Alternating Algorithm for Solving 3D Exterior Helmholtz Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Qing Chen ◽  
Baoqing Liu ◽  
Qikui Du
Keyword(s):  
Domain Decomposition Method ◽  
Three Dimensional ◽  
Boundary Element Methods ◽  
The Finite Element Method ◽  
Natural Boundary ◽  
Artificial Boundary ◽  
Nonoverlapping Domain ◽  
Helmholtz Problem ◽  
Nonoverlapping Domain Decomposition ◽  
Dimensional Domain

The nonoverlapping domain decomposition method, which is based on the natural boundary reduction, is applied to solve the exterior Helmholtz problem over a three-dimensional domain. The basic idea is to introduce a spherical artificial boundary; the original unbounded domain is changed into a bounded subdomain and a typical unbounded region; then, a Dirichlet-Nuemann (D-N) alternating method is presented; the finite element method and natural boundary element methods are alternately applied to solve the problems in the bounded subdomain and the typical unbounded subdomain. The convergence of the D-N alternating algorithm and its discretization are studied. Some numerical experiments are presented to show the performance of this method.

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