An Introduction to Meshless Methods with Applications in Engineering

This textbook provides a structured introduction to meshless methods, with a particular emphasis on engineering applications. It covers the fundamentals of numerical modelling, including strong, weak, and hybrid formulations, and presents detailed approaches for solving partial differential equations using three different meshless methods.

This textbook provides a structured introduction to meshless methods, with a particular emphasis on engineering applications. It covers the fundamentals of numerical modelling, including strong, weak, and hybrid formulations, and presents detailed approaches for solving partial differential equations (PDEs) using three different meshless methods. Readers will gain practical insights through MATLAB codes that can be adapted to a wide range of engineering problems, including groundwater flow and contaminant transport. Key FeaturesOffers simplified yet effective explanations that enable readers to develop meshless models with a limited mathematical background. Includes step-by-step formulations and MATLAB codes for solving elliptic, parabolic, and hyperbolic PDEs using three meshless methods representing the strong, weak, and hybrid formulation categories. Summarizes the challenges encountered in three-dimensional (3D) simulations and demonstrates how meshless methods can help overcome these challenges. Highlights state-of-the-art developments and identifies potential research opportunities in the field of meshless methods. Contains numerous examples from various disciplines, including worked examples and accompanying codes. The simplified mathematical frameworks enhance accessibility, making this textbook ideal for senior undergraduate and postgraduate students in civil and mechanical engineering, as well as practicing engineers seeking practical guidance on meshless modelling techniques.