scholarly journals GPU COMPUTING FOR 2D WAVE EQUATION BASED ON IMPLICIT FINITE DIFFERENCE SCHEMES

2020 ◽  
Vol 3 (77) ◽  
pp. 32-41
Author(s):  
A. Altybay ◽  
◽  
N. Tokmagambetov ◽  
Z. Spabekova ◽  
◽  
...  
Keyword(s):  
Wave Equation ◽  
Approximate Solution ◽  
Finite Difference ◽  
Gpu Computing ◽  
Fundamental Equation ◽  
Finite Difference Schemes ◽  
Special Focus ◽  
Central Processor ◽  
Finite Difference Equations ◽  
Parallel Code

In this paper we will consider the numerical implementation of the 2d wave equation which is a fundamental equation in many engineering problems. An approximate solution of a function is calculated from discrete points in spatial grid based on discrete time steps. The initial values are given by the initial value condition. First we will interpret how to transform a differential equation into an implicit finitedifference equation, respectively, a set of finite-difference equations that can be used to calculate an approximate solution. Then we will change this algorithm to parallelize this task on GPU. Special focus is on improving the performance of the parallel algorithm. In addition, we will run the implemented parallel code on the GPU and serial code the central processor, calculate the acceleration based on the execution time. We present that the parallel code that runs on a GPU gives the expected results by comparing our results to those obtained by running serial code of the same simulation on the CPU. In fact, in some cases, simulations on the GPU are found to run 22 times faster than on a CPU

Optimal Finite Analytic Methods

1982 ◽  
Vol 104 (3) ◽  
pp. 432-437 ◽  
Author(s):  
R. Manohar ◽  
J. W. Stephenson
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Linear Combination ◽  
Difference Equations ◽  
New Method ◽  
Linear Partial Differential Equations ◽  
Finite Difference Equations

A new method is proposed for obtaining finite difference equations for the solution of linear partial differential equations. The method is based on representing the approximate solution locally on a mesh element by polynomials which satisfy the differential equation. Then, by collocation, the value of the approximate solution, and its derivatives at the center of the mesh element may be expressed as a linear combination of neighbouring values of the solution.

Calculation of External and Internal Transonic Flow Field of a Three-Dimensional S-Shaped Inlet

1985 ◽  
Author(s):  
Shen Huili ◽  
Luo Shijun ◽  
Ji Minggang ◽  
Xing Zongwen ◽  
Zhu Xin ◽  
...  
Keyword(s):  
Finite Difference ◽  
Flow Field ◽  
Transonic Flow ◽  
Present Method ◽  
Velocity Potential ◽  
Free Stream ◽  
Three Dimensional ◽  
Finite Difference Schemes ◽  
Finite Difference Equations ◽  
Free Stream Mach Number

A mixed finite difference method for calculating the external and internal transonic flow field around an s-shaped inlet is presented. Starting from the velocity potential equation and using Cartesian mesh and mixed finite difference schemes, the authors have obtained a system of finite difference equations and solved them with the aid of alternating line relaxations along two directions. Computations have been made for an s-shaped inlet with free stream Mach number M=0.8 at different angles of attack. Computed results are compared with those computed by perturbation method and with experimental results. Such a comparison shows that the present method is promising.

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