Monte Carlo Methods for Partial Differential Equations With Applications to Electronic Design Automation

The Monte Carlo method is one of the top 10 algorithms in the 20th century. This book is focusing on the Monte Carlo method for solving deterministic partial differential equations (PDEs), especially its application to electronic design automation (EDA) problems. Compared with the traditional method, the Monte Carlo method is more efficient when point values or linear functional of the solution are needed, and has the advantages on scalability, parallelism, and stability of accuracy. This book presents a systematic introduction to the Monte Carlo method for solving major kinds of PDEs, and the detailed explanation of relevant techniques for EDA problems especially the cutting-edge algorithms of random walk based capacitance extraction. It includes about 100 figures and 50 tables, and brings the reader a close look to the newest research results and the sophisticated algorithmic skills in Monte Carlo simulation software.

Focuses on using the Monte Carlo method for solving deterministic PDEs Presents a Monte Carlo algorithm for a special hyperbolic PDE Provides fast random walk methods for solving elliptic and parabolic PDEs

Autorentext

Dr. Wenjian Yu is a Full Professor with the Department of Computer Science and Technology, Tsinghua University, Beijing, China. Dr. Yu's current research interests include physical-level modelling and simulation techniques for IC design, high-performance numerical algorithms, and Big-Data analytics and machine learning. Dr. Yu has authored/coauthored two books and about 200 papers in refereed journals and conferences. He was the recipient of the distinguished Ph.D. Award from Tsinghua University in 2003, the Excellent Young Scientist Award from the National Science Foundation of China in 2014. He received the Best Paper Awards of DATE'2016, ACES'2017 and ICTAI'2019, and 6 Best Paper Award Nominations in ICCAD, DATE, ASPDAC, ISQED and GLSVLSI.

Inhalt
Introduction.- Monte Carlo Method for Solving PDE.- A Monte Carlo Algorithm for the Telegrapher's Equations.- Basics of Floating Random Walk Method for Capacitance Extraction.- Pre-Characterization Techniques for FRW Based Capacitance Extraction.- Fast FRW Solver for 3-D Structures with Cylindrical Inter-Tier-Vias.- Fast FRW Solver for Structures with Non-Manhattan Conductors.- Technique for Capacitance Simulation with General Floating Metals.- Markov-Chain Random Walk and Macromodel-Aware Capacitance Extraction.- GPU-Friendly FRW Algorithm for Capacitance Extraction.- Distributed Parallel FRW Algorithm for Capacitance Simulation.- A Hybrid Random Walk Algorithm for 3-D Thermal Analysis.