IMPLEMENTING HYBRID PDE SOLVERS [dataset]

Manolis Vavalis
2014 Figshare  
We investigate the possibility that we effectively combine both conventional deterministic PDE solving methods and traditional probabilistic Monte Carlo approaches for solving linear Elliptic Partial Differential Equations. Our objective is to provide a robust and easy to use implementation that allows further experimentation on this new type of PDE solvers in order to elucidate their capabilities and computational characteristics. We first present the general formulation of the algorithm, then
more » ... the algorithm, then describe its implementation in C++ for a class of model problems in two and three space dimensions, we analyze its performance and we finally discuss possible extensions.
doi:10.6084/m9.figshare.1134520.v1 fatcat:lyoigcn2kvdebpn6s7uk46icke