GaspiLS – Scalability for CFD and FEM Simulations

Optimal Use of Given Computing Resources

In order to achieve better scalability, GaspiLS uses tools for parallel programming which are developed by us: These are the communication library GPI-2 and its underlying programming model. The algorithm is split into fine grained sub problems (so-called tasks) with mutual dependencies. This allows for the assignment of executable tasks to free compute resources at any time and guarantees for a continuous stream of compute tasks for every CPU.

In this way, we avoid global synchronization points and compensate for the latency times or imbalances in compute time resulting from the exchange of data due to the large number of generated sub problems. Every single core is maximally emploited at any time.

Preconditioner

Preconditioners are designed to improve the convergence of iterative Krylov subspace solvers, i.e. they reduce the number of required iterations or are even a necessary condition to solve a given problem at all. Therefore, beside the absolute performance and scalability of the basic solvers provided by GapiLS, preconditioners are a key component to solve sparse linear systems efficiently.

GaspiLS provides two classes of black-box preconditioners, now. Algebraic Multigrid (AMG) for symmetric positive definite problems as they appear e.g. in CFD applications and Multi-Level Incomplete LU (Multi-Level ILU) factorizations as a generic preconditioner. Both implementations follow a scalable, efficient, hybrid parallel Gaspi-based approach.

AMG, as representative of a multigrid method, has a linear computational complexity, which is optimal. It can be applied to symmetric positive definite problems. In AMG, a hierarchy of operators is directly constructed from the linear system, without explicit knowledge of the underlying geometry or partial differential equation.

Multi-Level ILU, on the other hand, is widely used because of its robustness, accuracy, and usability as a black-box preconditioner for general sparse linear systems. ILU consists of LU based Gaussian elimination combined with dropping. Depending on the chosen input parameters and the amount of available resources, Multi-Level ILU allows for seemless interpolation between full Gaussian elimination on one end (exact inverse, high resource consumption) and Jacobi preconditioning on the other end (low resource consumption, low quality). Our implementation supports row and col based permutation in the factorization which is often needed to solve a linear system with ill-conditioned matrices.

GaspiCxx for Increased Productivity

Within GaspiLS, we have factorized the implementation for the explicit management of communication resources required by the GPI-2 data transfer and used GaspiCxx to supply it to other applications. GaspiCxx defines an easy to use C++ interface. It delivers the full native GPI-2 performance. At the same time, the management of GPI-2 communication resources is fully transparent to the application. This eliminates a large part of the implementation work normally required to develop GPI-2 applications. Development of GPI-2 applications and the exploitation of the advantages – like the good scalability – has never been so easy.