Parallel tridiagonal matrix inversion with a hybrid multigrid-Thomas algorithm method

Tridiagonal matrix inversion is an important operation with many applications. It arises frequently in solving discretized one-dimensional elliptic partial differential equations, and forms the basis for algorithms block tridiagonal PDEs higher-dimensions. In such systems, this often scaling bottleneck parallel computation. paper, we derive a hybrid multigrid-Thomas algorithm designed to efficiently invert equations highly-scalable fashion context of time evolving equation systems. We decompose domain between processors, using multigrid solve on grid consisting boundary points each processor’s local domain. then reconstruct solution processor direct Thomas algorithm. This has same theoretical optimal as cyclic reduction recursive doubling. use our Poisson’s part spatial discretization time-evolving PDE system. Our faster than per retains good efficiency twice cores.