Solvers for systems of large sparse linear and nonlinear equations based on multi-GPUs

Numerical treatment of engineering application problems often eventually results in a solution of systems of linear or nonlinear equations. The solution process using digital computational devices usually takes tremendous time due to the extremely large size encountered in most real-world engineering applications. So, practical solvers for systems of linear and nonlinear equations based on multi graphic process units (GPUs) are proposed in order to accelerate the solving process. In the linear and nonlinear solvers, the preconditioned bi-conjugate gradient stable (PBi-CGstab) method and the Inexact Newton method are used to achieve the fast and stable convergence behavior. Multi-GPUs are utilized to obtain more data storage that large size problems need.