Local Numerical Solutions in Solid Mechanics

Cornell University, Ithaca NY

Investigators

Abstract

LOCAL NUMERICAL SOLUTIONS IN SOLID MECHANICS Mircea Grigoriu and Subrata Mukherjee Cornell University Local numerical methods, based on Monte Carlo simulations, directly deliver the value of an unknown function at a point inside a domain without the need for calculating its value at any other point. No meshing is required, no linear equation systems need to be solved and the method is very easy to code and parallelize. This class of methods includes the Random 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.