Monte Carlo Methods For Partial Differential Equations With Applications To Electronic Design Automation Wenjian Yu by Wenjian Yu, Michael Mascagni 9789811932496, 9811932492 instant download after payment.

The main purpose of this book is to present a systematic and algorithmic perspective on the Monte Carlo method for solving partial differential equations (PDEs), especially their fast algorithms and practical applications. We will focus mainly on elliptic PDEs, i.e., the Laplace and Poisson equations describing equilibrium states. Moreover, the applications that motivate us will mainly come from microelectronic integrated circuit. The Monte Carlo method in the Russian literature is often referred to (in translation) as “the method of statistical sampling.” This phrase has much more meaning than “the Monte Carlo method,” which was chosen due to the famous casino in Monte Carlo. Monte Carlo can be used to solve a variety of problems, and is the basis of the areas of stochastic ordinary differential equations (ODEs) and PDEs, and uncertainty quantification. In this book, we focus on the Monte Carlo method for solving partial differential and integral equations based on random walks. The random walk method essentially involves the Markov process...