A mesh-free method with arbitrary-order accuracy for acoustic wave propagation

Abstract

a b s t r a c tIn the present study, we applied a novel mesh-free method to solve acoustic wave equation. Although the conventional finite difference methods determine the coefficients of its operator based on the regular grid alignment, the mesh-free method is not restricted to regular arrangements of calculation points. We derive the mesh-free approach using the multivariable Taylor expansion. The methodology can use arbitrary-order accuracy scheme in space by expanding the influence domain which controls the number of neighboring calculation points. The unique point of the method is that the approach calculates the approximation of derivatives using the differences of spatial variables without parameters as e.g. the weighting functions, basis functions. Dispersion analysis using a plane wave reveals that the choice of the higher-order scheme improves the dispersion property of the method although the scheme for the irregular distribution of the calculation points is more dispersive than that of the regular alignment. In numerical experiments, a model of irregular distribution of the calculation points reproduces acoustic wave propagation in a homogeneous medium same as that of a regular lattice. In an inhomogeneous model which includes low velocity anomalies, partially fine arrangement improves the effectiveness of computational cost without suffering from accuracy reduction. Our result indicates that the method would provide accurate and efficient solutions for acoustic wave propagation using adaptive distribution of the calculation points.

An adaptive resolution full-waveform inversion using a mesh-free finite-difference method

“…(1) Mesh-free FD method Figure 1 shows an example of the acoustic wave propagation using the mesh-free FD method 2) . The method enables us to simulate wave propagation using irregular arrangement of calculation points.…”

“…In the present study, we apply a mesh-free method 2) as a full-wavefield simulator. The method can provide full-wavefield without mesh or regular lattice.…”

Frequency-domain mesh-free finite-difference operator for visco-acoustic wave equation

“…The details of the derivation of the above equations can be found in a reference 4) . As an absorbing boundary condition (ABC), we apply a hybrid technique for the frequency-domain modeling 6,7) .…”

“…In the present study, we apply the mesh-free method 4) as a simulator in the frequency-domain modeling. To evaluate the effectiveness of the MF-FDM, we conduct a numerical experiment using a low velocity anomaly model.…”

An absorbing boundary condition for acoustic-wave propagation using a mesh-free method

“…The pursuit of the computational efficiency in a mesh-free framework has led to the simulation of acoustic-wave propagation with arbitrary high-order accuracy using the spatial resolution suitable for the velocity structure of a model, i.e., nonregular spacing between neighboring nodes to estimate physical values (Takekawa et al, 2015). Mesh-free methods provide efficient simulations without the use of a mesh structure in popular grid-based methods and enable us to arrange particles or calculation points adaptively to a computational region in a highly flexible way.…”