**hypre: A Library of High Performance Preconditioners** **Authors:** Robert D. Falgout and Ulrike Meier Yang **Affiliation:** Center for Applied Scientific Computing, Lawrence Livermore National Laboratory **Abstract:** hypre is a software library designed for solving large, sparse linear systems on massively parallel computers, focusing on modern, powerful, and scalable preconditioners. The library provides various conceptual interfaces to facilitate user access based on their problem-solving approaches. This paper introduces these interfaces and provides an overview of the preconditioners available in hypre, including numerical results demonstrating their efficiency. **Introduction:** The increasing demands of computationally intensive applications and advancements in computer architecture necessitate the development of new solvers and preconditioners. hypre aims to provide advanced, scalable parallel preconditioners with robustness, ease of use, flexibility, and interoperability. It can be used as a solver package or a framework for algorithm development. hypre supports several commonly used solvers, such as conjugate gradient and GMRES, and offers multiple conceptual interfaces to accommodate different problem formulations, including structured grids, semi-structured grids, finite elements, and linear algebraic systems. **Conceptual Interfaces:** - **Structured-Grid System Interface (Struct):** Suitable for scalar applications with logically rectangular grids and fixed stencil patterns. - **Semi-Structured-Grid System Interface (SStruct):** For applications with mostly structured grids but some unstructured features. - **Finite Element Interface (FEI):** For finite element discretizations, mirroring typical finite element data structures. - **Linear-Algebraic System Interface (IJ):** The traditional linear algebraic interface, requiring users to define the right-hand side and matrix in terms of row and column indices. **Preconditioners:** - **SMG (Semicoarsening Multigrid):** A parallel solver for diffusion equations on logically rectangular grids, robust and efficient. - **PFMG (Parallel Fine-Mesh Multigrid):** Similar to SMG but less robust but more efficient per V-cycle. - **BoomerAMG (Algebraic Multigrid):** A parallel implementation of algebraic multigrid, using two types of coarsening strategies and various smoothers. - **ParaSails (Sparse Approximate Inverse):** A parallel sparse approximate inverse preconditioner, efficient for many problems. - **PILUT (Parallel Incomplete LU Factorization):** A parallel preconditioner based on Saad's dual-threshold incomplete factorization algorithm. - **Euclid (Parallel ILU):** A scalable implementation of the Parallel ILU algorithm, supporting various variants of ILU($k$) and ILUT preconditionings. **Conclusions and Future Work:** hypre continues to evolve with new research leading to better and more efficient algorithms. Future developments include the addition of AMGe, an algebraic multigrid method based on local finite element stiffness matrices,**hypre: A Library of High Performance Preconditioners** **Authors:** Robert D. Falgout and Ulrike Meier Yang **Affiliation:** Center for Applied Scientific Computing, Lawrence Livermore National Laboratory **Abstract:** hypre is a software library designed for solving large, sparse linear systems on massively parallel computers, focusing on modern, powerful, and scalable preconditioners. The library provides various conceptual interfaces to facilitate user access based on their problem-solving approaches. This paper introduces these interfaces and provides an overview of the preconditioners available in hypre, including numerical results demonstrating their efficiency. **Introduction:** The increasing demands of computationally intensive applications and advancements in computer architecture necessitate the development of new solvers and preconditioners. hypre aims to provide advanced, scalable parallel preconditioners with robustness, ease of use, flexibility, and interoperability. It can be used as a solver package or a framework for algorithm development. hypre supports several commonly used solvers, such as conjugate gradient and GMRES, and offers multiple conceptual interfaces to accommodate different problem formulations, including structured grids, semi-structured grids, finite elements, and linear algebraic systems. **Conceptual Interfaces:** - **Structured-Grid System Interface (Struct):** Suitable for scalar applications with logically rectangular grids and fixed stencil patterns. - **Semi-Structured-Grid System Interface (SStruct):** For applications with mostly structured grids but some unstructured features. - **Finite Element Interface (FEI):** For finite element discretizations, mirroring typical finite element data structures. - **Linear-Algebraic System Interface (IJ):** The traditional linear algebraic interface, requiring users to define the right-hand side and matrix in terms of row and column indices. **Preconditioners:** - **SMG (Semicoarsening Multigrid):** A parallel solver for diffusion equations on logically rectangular grids, robust and efficient. - **PFMG (Parallel Fine-Mesh Multigrid):** Similar to SMG but less robust but more efficient per V-cycle. - **BoomerAMG (Algebraic Multigrid):** A parallel implementation of algebraic multigrid, using two types of coarsening strategies and various smoothers. - **ParaSails (Sparse Approximate Inverse):** A parallel sparse approximate inverse preconditioner, efficient for many problems. - **PILUT (Parallel Incomplete LU Factorization):** A parallel preconditioner based on Saad's dual-threshold incomplete factorization algorithm. - **Euclid (Parallel ILU):** A scalable implementation of the Parallel ILU algorithm, supporting various variants of ILU($k$) and ILUT preconditionings. **Conclusions and Future Work:** hypre continues to evolve with new research leading to better and more efficient algorithms. Future developments include the addition of AMGe, an algebraic multigrid method based on local finite element stiffness matrices,