This book presents methods for full-wave computer simulation that can be used in various applications and contexts, e.g. seismic prospecting, earthquake stability, global seismic patterns on Earth and Mars, medicine, traumatology, ultrasound investigation of the human body, ultrasound and laser operations, ultrasonic non-destructive railway testing, modelling aircraft composites, modelling composite material delamination, etc. The key innovation of this approach is the ability to study spatial dynamical wave processes, which is made possible by cutting-edge numerical finite-difference grid-characteristic methods. The book will benefit all students, researchers, practitioners and professors interested in numerical mathematics, computer science, computer simulation, high-performance computer systems, unstructured meshes, interpolation, seismic prospecting, geophysics, medicine, non-destructive testing and composite materials.