scholarly journals Wave gradiometry and its link with Helmholtz equation solutions applied to USArray in the eastern U.S.

2015 ◽  
Vol 120 (8) ◽  
pp. 5717-5746 ◽  
Author(s):  
Yuanyuan Liu ◽  
William E. Holt
Keyword(s):  
Helmholtz Equation ◽  
Wave Gradiometry

A preconditioned method for the solution of the Robbins problem for the Helmholtz equation

2011 ◽  
Vol 51 ◽  
pp. 87
Author(s):  
Jiang Le ◽  
Huang Jin ◽  
Xiao-Guang Lv ◽  
Qing-Song Cheng
Keyword(s):  
Helmholtz Equation

scholarly journals Gravitational Interaction in the Chimney Lattice Universe

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 101
Author(s):  
Maxim Eingorn ◽  
Andrew McLaughlin ◽  
Ezgi Canay ◽  
Maksym Brilenkov ◽  
Alexander Zhuk
Keyword(s):  
Helmholtz Equation ◽  
Gravitational Potential ◽  
Fourier Expansion ◽  
Gravitational Interaction ◽  
Alternative Solution ◽  
The Third ◽  
Present Universe ◽  
Delta Functions ◽  
Yukawa Potentials ◽  
The Universe

We investigate the influence of the chimney topology T×T×R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.

An iterative solver for the 3D Helmholtz equation

2017 ◽  
Vol 345 ◽  
pp. 330-344 ◽  
Author(s):  
Mikhail Belonosov ◽  
Maxim Dmitriev ◽  
Victor Kostin ◽  
Dmitry Neklyudov ◽  
Vladimir Tcheverda
Keyword(s):  
Helmholtz Equation ◽  
Iterative Solver
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