This book provides a comprehensive introduction to the finite-difference time-domain (FDTD) method, a widely used numerical technique for simulating wave propagation and related physical phenomena. It equips readers with the theoretical foundations and practical tools needed to develop their own transparent, modular simulation codes. Covering electromagnetic, acoustic, magnonic, sociophysical, quantum and mechanical systems, as well as coupled multiphysics processes, the book progresses from fundamental principles to advanced applications and provides ready-to-use algorithms and examples that can be executed on modest hardware. It serves as both a reference and a practical guide for those seeking to understand and extend FDTD methods in research and development.

• Presents a multiphysics FDTD framework covering electromagnetic, acoustic, magnonic, sociophysical, quantum and mechanical phenomena
• Explores unconventional applications of multiphysics FDTD through original case studies and practical examples
• Provides ready-to-use algorithms and transparent, modular computer codes designed to run efficiently on standard desktop and laptop hardware, as well as GPUs, FPGA accelerators and resource-constrained hardware

Ivan S. Maksymov began his academic journey at the renowned Kharkov Physics School, founded by Nobel Laureate Lev Landau, and continued his research at one of Europe’s leading centres for optics and photonics. He later held the prestigious Australian Research Council Future Fellowship, establishing a reputation as a versatile and innovative scientist and earning recognition among the world’s top 2% of researchers. His research has also inspired popular-science articles for general audiences. In 2020, he received the Ig Nobel Prize in Physics.