scholarly journals Exact extrapolation and immersive modelling with finite-difference injection

2020 ◽  
Vol 223 (1) ◽  
pp. 584-598
Author(s):  
Dirk-Jan van Manen ◽  
Xun Li ◽  
Marlies Vasmel ◽  
Filippo Broggini ◽  
Johan Robertsson

SUMMARY In numerical modelling of wave propagation, the finite-difference (FD) injection method enables the re-introduction of simulated wavefields in model subdomains with machine precision, enabling the efficient calculation of waveforms after localized model alterations. By rewriting the FD-injection method in terms of sets of equivalent sources, we show how the same principles can be applied to achieve on-the-fly wavefield extrapolation using Kirchhoff–Helmholtz (KH)-like integrals. The resulting extrapolation methods are numerically exact when used in conjunction with FD-computed Green’s functions. Since FD injection only relies on the linearity of the wave equation and compactness of FD stencils in space, the methods can be applied to both staggered and non-staggered discretizations with arbitrary-order spatial operators. Examples for both types of discretizations show how these extrapolators can be used to truncate models with exact absorbing or immersive boundary conditions. Such immersive modelling involves the evaluation of KH-type extrapolation and representation integrals in the same simulation, which include the long-range interactions missing from conventional FD injection.

2006 ◽  
Vol 16 (06) ◽  
pp. 1645-1669 ◽  
Author(s):  
SERGEJ FLACH ◽  
ANDREY GORBACH

This work provides a description of the main computational tools for the study of discrete breathers. It starts with the observation of breathers through simple numerical runs, the study uses targeted initial conditions, and discrete breather impact on transient processes and thermal equilibrium. We briefly describe a set of numerical methods to obtain breathers up to machine precision. In the final part of this work we apply the discussed methods to study the competing length scales for breathers with purely anharmonic interactions — favoring superexponential localization — and long range interactions, which favor algebraic decay in space. As a result, we observe and explain the presence of three different spatial tail characteristics of the considered localized excitations.


2003 ◽  
Vol 2003 (2) ◽  
pp. 1-4
Author(s):  
James Sun ◽  
Carl Notfors ◽  
Zhang Yu ◽  
Gray Sam ◽  
Young Jerry

Author(s):  
Hideyo Yoshida ◽  
Takefumi Hayashi

In the present research, we developed an interactive numerical simulation system for evaluation of static and dynamic characteristics of a flying head slider under nano-meter spacing conditions. This system enables rapid and efficient calculation while changing parameters that affect the numerical solution of the fundamental equations. The system also supports several types of sliders and patterned disk surfaces as well. Furthermore, the upstream finite difference method is applied to the Couette flow term instead of the conventional central finite difference method, and the convergence of the pressure solution is found to be much improved.


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