Abstract
Abstract Many important natural phenomena of wave propagations are modeled by Eikonal equations and a variety of new methods are needed to solve them. The differential quadrature method (DQM) is an effective numerical method for solving the system of differential equations that can achieve accurate numerical results using fewer grid points and therefore requires relatively little computational effort. In this paper, we focus on the implementation of the non-smooth Eikonal optimization by using a hybrid of polynomial differential quadrature (PDQ) or Fourier differential quadrature (FDQ) method and sub-gradients idea. Our goal is to develop a new Eikonal equation system design for wave propagation equations, as well as the efficiency and accuracy of new grid points to reduce errors and compare errors in various physical equation problems, especially wave propagation equations, and achieve their convergence. We explore the accuracy and stability of the Eikonal equation system by two-dimensional and three-dimensional numerical examples and the use of three types of grid points in a comprehensive manner. This article aims to create a new and innovative solution to the non-smooth Eikonal equation system. This new method is much more efficient and effective than traditional numerical solution methods same as DQ.
Highlights
Many important natural phenomena of wave propagations are modeled by Eikonal equations and a variety of new methods are needed to solve them
We focus on the implementation of the non-smooth Eikonal optimization by using a hybrid of polynomial differential quadrature (PDQ) or Fourier differential quadrature (FDQ) method and sub-gradients idea
Our goal is to develop a new Eikonal equation system design for wave propagation equations, as well as the efficiency and accuracy of new grid points to reduce errors and compare errors in various physical equation problems, especially wave propagation equations, and achieve their convergence
Summary
Abstract: Many important natural phenomena of wave propagations are modeled by Eikonal equations and a variety of new methods are needed to solve them. In this paper we want to use a combination of two methods (subgradient and differential quadrature) to solve the system of Eikonal equations. Because these methods are easy to implement and have a relatively low computational cost. Each of these issues can be a model of wave propagation equations, which is an important physical phenomenon that has been presented by the true solution of the system of equations or as a field of velocity. To compare the accuracy of the errors, we have shown the error plots of the PDQ and FDQ methods in the figures and in Section 6, the results are summarized
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