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a Configuration of 2D finite difference simulations using e3d (Larsen and Shultz 1995).

We developed and demonstrated the use of an effective absorbing boundary condition for finite difference simulation of tsunamis.

The results of our numerical experiments using finite difference simulations with a realistic 3D inhomogeneous medium model, together with the application of the method to real-world data, show that we can reconstruct a continuous and coherent wavefield with a period longer than 25 s by applying seismic gradiometry to Hi-net records.

To interpret these observations, we conducted 2D finite difference simulations.

Forward model simulations are computed using finite difference equations generated using Maxwell's equation or computed using Divided Difference method using Taylor series ( PBG Report 2014).

Fluid mixing in steady and unsteady flow through a channel containing periodic square obstructions has been studied using a finite-difference simulation to determine fluid velocities, followed by the use of passive marker particle advection to look at fluid transport out of the cavities formed between each of the obstructions.

Through a three-dimensional finite difference time domain (FDTD) simulation (using a commercial software from Lumerical Inc), we have proved that at this thickness, the red-shifts of SPR peaks are mainly caused by their surface roughness, and the hollow nature of these particles plays only a minor role [17].

To evaluate a reliability of the calculated results by the TM method, we conducted a finite-difference time-domain (FDTD) simulation using the model with the Ag nanoparticle structures (Fig. S3).

The results of simulation using finite difference time domain (FDTD) method shows this structure have a good performances and reveals an average transmitted power is higher than 95%, channel spacing is about 6.1 nm and bandwidth for each individual channel is about 2.75 nm.

It is important to note, when creating a geomechanical model, the finite difference mesh used in the fluid flow simulation and the finite element mesh used for the stress analysis, are not coincident.

The results of simulation using finite-difference time-domain (FDTD) method in our proposed structure reveals an average transmitted power higher than 90% for each output port, Channel spacing is about 8 nm and bandwidth for each individual channel is about 2.8 nm.