This unique compendium presents the Gradient Smoothing Methods (GSMs), as a general solver for linear and nonlinear PDEs (Partial Differential Equations) with a focus on fluids and flowing solids.The volume introduces the basic concepts and theories of the gradient smoothing technique used in the GSMs. Formulations for both Eulerian-GSM and Lagrangian-GSM are presented. The key ingredients of GSMs and its effectiveness in solving challenging fluid/solid flow problems with complex geometries are then discussed.Applications of GSM are highlighted, including compressible and incompressible flows, hydrodynamics with flexible free surface, and flowing solids with material strength and large deformation in geotechnical engineering, in particular, landslide simulations.In-house MATLAB codes are provided for both Eulerian and Lagrangian GSMs, along with detailed descriptions. More efficient FORTRAN source codes for solving complex engineering problems are also available on Github.

This is the first-ever book on smoothed particle hydrodynamics (SPH) and its variations, covering the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications. It contains many appealing and practical examples, including free surface flows, high explosive detonation and explosion, underwater explosion and water mitigation of explosive shocks, high velocity impact and penetration, and multiple scale simulations coupled with the molecular dynamics method. An SPH source code is provided and coupling of SPH and molecular dynamics is discussed for multiscale simulation, making this a friendly book for readers and SPH users.

Machine Learning (ML) has become a very important area of research widely used in various industries.This compendium introduces the basic concepts, fundamental theories, essential computational techniques, codes, and applications related to ML models. With a strong foundation, one can comfortably learn related topics, methods, and algorithms. Most importantly, readers with strong fundamentals can even develop innovative and more effective machine models for his/her problems. The book is written to achieve this goal.The useful reference text benefits professionals, academics, researchers, graduate and undergraduate students in AI, ML and neural networks.

Multi-scale and multi-physics modeling is useful and important for all areas in engineering and sciences. Particle Methods for Multi-Scale and Multi-Physics systematically addresses some major particle methods for modeling multi-scale and multi-physical problems in engineering and sciences. It contains different particle methods from atomistic scales to continuum scales, with emphasis on molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH).This book covers the theoretical background, numerical techniques and many interesting applications of the particle methods discussed in this text, especially in: micro-fluidics and bio-fluidics (e.g., micro drop dynamics, movement and suspension of macro-molecules, cell deformation and migration); environmental and geophysical flows (e.g., saturated and unsaturated flows in porous media and fractures); and free surface flows with possible interacting solid objects (e.g., wave impact, liquid sloshing, water entry and exit, oil spill and boom movement). The presented methodologies, techniques and example applications will benefit students, researchers and professionals in computational engineering and sciences.

Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations - one of the most important features of the next generation methods. This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds. The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development.