Ifpack2Edit

Ifpack2 is a software package within the Trilinos project that supplies a flexible suite of algebraic preconditioners for solving large sparse linear systems on modern high-performance computing platforms. It is designed to work with distributed-memory architectures and integrates tightly with the Tpetra linear algebra interface, while leveraging the performance portability of Kokkos to run efficiently on CPUs and accelerators alike. The library is widely used in scientific and engineering simulations to accelerate Krylov subspace methods such as GMRES, CG, and BiCGStab that arise in the discretization of partial differential equations and related problems.

Ifpack2 serves as a modern, architecture-aware successor to earlier preconditioning components and is built to fit into the broader Trilinos ecosystem. By providing a rich set of preconditioners and composable building blocks, it gives developers and researchers a way to tailor solver pipelines to their problem characteristics and hardware. See also Trilinos for the broader project context and Ifpack for the historical lineage of these methods.

Overview

Purpose and scope: Ifpack2 implements a collection of algebraic preconditioners that operate directly on sparse matrices, without requiring explicit knowledge of the underlying discretization. This makes them broadly applicable across applications and problem domains. See sparse matrix for the data structures typically involved.
Integration points: The preconditioners are designed to work with common iterative solvers in the Trilinos ecosystem, especially those provided by Tpetra and compatible with distributed memory execution. They can be composed with other solver components to form end-to-end solution strategies.
Architecture and portability: The library uses Kokkos to achieve performance portability across different hardware backends, including multi-core CPUs and GPUs. This design supports a range of execution spaces and memory models while preserving a consistent programming model.

Algorithms and features

Range of preconditioners: Ifpack2 offers ILU-type methods (including incomplete LU factorizations with various fill-in settings), IC (incomplete Cholesky for symmetric positive-definite systems), and ILUT-like variants. It also includes Jacobi and block-Jacobi relaxations, as well as block-relaxation schemes and domain-decomposition approaches such as Additive Schwarz for parallel scalability.
Tuning and configurability: Users control behavior via a parameter list (often referred to as a ParameterList) that sets aspects such as fill level, drop tolerance, relaxation schemes, and subdomain solver choices. This configurability lets practitioners trade off speed, memory usage, and robustness for their specific problem.
Coupling with solvers: Preconditioners supplied by Ifpack2 are intended to accelerate Krylov methods like GMRES, the Conjugate gradient method, and other iterative solvers. By reducing the condition number or clustering eigenvalues, these preconditioners improve convergence rates and overall wall-clock time.
Data model compatibility: Implementations operate on the matrices and vectors provided by Tpetra (and, historically, related interfaces in the Trilinos family). This alignment helps ensure compatibility with a wide range of discretizations and solver configurations.

Architecture and design

Template-driven design: Ifpack2 is written with templates to support various scalar types, local and global index types, and execution spaces. This approach enables it to work across different problem sizes and arithmetic precision settings.
Separation of concerns: The library cleanly separates the definition of preconditioner objects from the data structures they consume. This makes it easier to plug in different matrix formats or subdomain solvers without rewriting the core framework.
Portability and performance: By building on Kokkos and MPI, Ifpack2 targets scalable performance on clusters and supercomputers. It aims to provide predictable behavior on heterogeneous systems while retaining a familiar API for users transitioning from older Trilinos components.
Ecosystem coherence: Ifpack2 follows the Trilinos philosophy of interoperable components. It can be used in concert with other packages such as Belos (the solver framework) and Ifpack (the historical predecessor), maintaining a broad compatibility surface for users.

Usage and interoperability

Getting started: Typical usage involves constructing a preconditioner object from a sparse matrix representation, configuring it via a ParameterList, and applying it as part of a solver workflow. This often includes choosing a subdomain solver or smoothing strategy appropriate for the problem.
Problem characteristics: The choice of preconditioner in Ifpack2 depends on matrix properties such as symmetry, sparsity pattern, and conditioning. For symmetric positives definite systems, IC-based strategies may be favored, while non-symmetric cases often benefit from ILU-type variants or domain-decomposition approaches.
Ecosystem interconnections: Beyond direct use with GMRES or CG, Ifpack2 can participate in more complex solver pipelines, enabling robust and scalable workflows for large-scale simulations. See also Tpetra for core matrix and vector abstractions and Kokkos for execution models.

Performance and scalability

Parallel scaling: With domain-decomposition and additive Schwarz-style preconditioners, Ifpack2 aims to achieve good weak and strong scaling on large processor counts by exploiting locality and overlap between subdomains.
Hardware considerations: The Kokkos-backed design provides portability to various backends, allowing performance tuning to be driven by back-end capabilities, vectorization, and memory bandwidth considerations. See also Kokkos for details on portability strategies.
Benchmarks and practice: In practice, the effectiveness of a given preconditioner depends on problem size, discretization, and hardware. Users typically experiment with a few representative configurations to determine which combination yields the best convergence and runtime balance for their application.