Local Numerical Solutions in Solid Mechanics

固体力学中的数值解基于Monte Carlo模拟的局部数值方法直接给出域内某点的未知函数值，而不需要计算其他任何点的值。该方法不需要网格划分，不需要求解线性方程组，易于编程和并行化。这类方法包括随机行走方法（RWM）、球面行走方法（WSM）和边界行走方法（BWM）。 本计画将发展局部方法来解决线弹性问题，然后是均匀化问题和随机边界问题。

LOCAL NUMERICAL SOLUTIONS IN SOLID MECHANICSMircea Grigoriu and Subrata MukherjeeCornell UniversityLocal numerical methods, based on Monte Carlo simulations, directlydeliver the value of an unknown function at a point inside a domain withoutthe need for calculating its value at any other point. No meshing isrequired, no linear equation systems need to be solved and the method isvery easy to code and parallelize. This class of methods includes theRandom Walk Method (RWM), the Walk on Spheres Method (WSM) and the Boundary Walk Method (BWM). Local methods will be developed in this project to solve linear elasticity problems, and then for homogenization problems and problems with random boundaries.