WaveGFD: Data and methods for numerically solving the wave equation using a meshless Generalized Finite Differences Scheme

Abstract

WaveGFD is a repository inspired by the development and analysis of meshless finite difference schemes for the wave equation in highly irregular domains, such as polygonal approximations of geographical regions.These methods' innovative approach allows to address the complexity of solving partial differential equations in highly irregular regions. They stand out for their precision and efficiency. The proposed methodology overcomes the limitations of conventional techniques, promising applicability in a broad spectrum of complex physical problems.The repository includes the methods necessary to find approximations to the solution of the wave equation, a set of test data consisting of clouds of points whose complexity varies from the unitary square (for comparison purposes) to regions that approximate actual geographic areas, examples of use, and results obtained with the proposed data and methods.WaveGFD considers the importance of having methods suitable for efficient implementations (i.e., that can be executed rapidly without the need for extensive and powerful computers) that can obtain satisfactory results when solving problems that may arise in different areas of engineering, such as civil and structural engineering (analysis of the vibrations in buildings and bridges), aerospace engineering (studies of the aeroelasticity of aircraft wings), electrical and telecommunications engineering (models of the propagation of electromagnetic waves), among others.

Keywords

• Meshless method
• Generalized finite difference
• Wave equation
• Irregular regions
• Numerical solution