Parallel and GPU-optimized linear solver for compact difference schemes

Compact finite difference methods are widely used for high-resolution simulations in many disciplines. The numerical method requires solving a cyclic tridiagonal or penta-diagonal system. For extreme-scale simulations, it is challenging to apply compact finite difference methods in a computationally-efficient way, particularly on devices with limited shared memory. Recently, a parallel linear solver algorithm for this purpose was developed and efficiently uses the capability of many-GPU distributed systems.

The presented work emphasizes algorithmic and implementation optimization strategies. The efforts are focused on achieving both scalability and absolute throughput. With this motivation, an open-source linear solver package is introduced to solve the linear systems arising from compact numerical schemes. The linear solver is implemented in the "MPI+X" paradigm, supporting various parallel processing units with portable performance. A set of uniform application programming interfaces (APIs) are provided. The solution process supports a partitioned 3D structured mesh. Raw pointers can pass the necessary data, providing compatibility with existing user code.