Order of Difference Expressions in Curvilinear Coordinate Systems

The order of finite difference representations on general curvilinear coordinate systems is considered in some detail. It is shown that the uniform grid order is formally preserved on the nonuniform, nonorthogonal grid in the sense of the error behavior with an increase in the number of points. However, the coefficients in the series expansion may become quite large for some point distributions. Several specific distributions are evaluated.

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Finite‐difference calculation of direct‐arrival traveltimes using the eikonal equation

Geophysics ◽

10.1190/1.1500389 ◽

2002 ◽

Vol 67 (4) ◽

pp. 1270-1274 ◽

Cited By ~ 5

Author(s):

Le‐Wei Mo ◽

Jerry M. Harris

Keyword(s):

Finite Difference ◽

Ray Tracing ◽

Finite Differences ◽

Eikonal Equation ◽

Velocity Model ◽

Uniform Grid ◽

Square Grid ◽

Kirchhoff Migration ◽

Difference Calculation

Traveltimes of direct arrivals are obtained by solving the eikonal equation using finite differences. A uniform square grid represents both the velocity model and the traveltime table. Wavefront discontinuities across a velocity interface at postcritical incidence and some insights in direct‐arrival ray tracing are incorporated into the traveltime computation so that the procedure is stable at precritical, critical, and postcritical incidence angles. The traveltimes can be used in Kirchhoff migration, tomography, and NMO corrections that require traveltimes of direct arrivals on a uniform grid.

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TOMCAT — A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies

Journal of Computational Physics ◽

10.1016/0021-9991(77)90038-9 ◽

1977 ◽

Vol 24 (3) ◽

pp. 274-302 ◽

Cited By ~ 189

Author(s):

Joe F Thompson ◽

Frank C Thames ◽

C Wayne Mastin

Keyword(s):

Two Dimensional ◽

Coordinate Systems ◽

Curvilinear Coordinate ◽

Numerical Generation

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Optimal staggered-grid finite-difference schemes by combining Taylor-series expansion and sampling approximation for wave equation modeling

Journal of Computational Physics ◽

10.1016/j.jcp.2016.09.019 ◽

2016 ◽

Vol 326 ◽

pp. 913-930 ◽

Cited By ~ 6

Author(s):

Hongyong Yan ◽

Lei Yang ◽

Xiang-Yang Li

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Series Expansion ◽

Taylor Series ◽

Taylor Series Expansion ◽

Difference Schemes ◽

Staggered Grid ◽

Equation Modeling ◽

Finite Difference Schemes

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Implementation of an Approximate Conformal UPML in 2-D DGTD

International Journal of Antennas and Propagation ◽

10.1155/2017/6358561 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Linqian Li ◽

Bing Wei ◽

Qian Yang ◽

Debiao Ge

Keyword(s):

Good Accuracy ◽

Computation Time ◽

Elliptic Cylinder ◽

Auxiliary Equation ◽

Coordinate Systems ◽

Absorbing Boundary ◽

Computational Region ◽

Curvilinear Coordinate ◽

Orthogonal Curvilinear Coordinate System ◽

Absorbing Layer

Using the numerical discrete technique with unstructured grids, conformal perfectly matched layer (PML) absorbing boundary in the discontinuous Galerkin time-domain (DGTD) can be set flexibly so as to save lots of computing resources. Based on the DGTD equations in an orthogonal curvilinear coordinate system, the processes of parameter transformation for 2-D UPML between the coordinate systems of elliptical and Cartesian are given; and the expressions of transition matrix are derived. The calculation scheme of conductivity distribution in elliptic cylinder absorbing layer is given, and the calculation coefficient of DGTD in elliptic UPML is calculated. Furthermore, the 2-D iterative formulas of DGTD and that of auxiliary equation in the elliptical cylinder UPML are derived; the conformal UPML calculation in DGTD is realized. Numerical results show that very good accuracy and computational efficiency are achieved by using the method in this paper. Compared to the rectangular computational region, both the memory and computation time of conformal UPML absorbing boundary are reduced by more than 20%.

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