Trilinos is a comprehensive software framework for scientific computing, providing a wide range of capabilities for solving complex engineering and scientific problems. Below is a categorized list of Trilinos capabilities with detailed descriptions.

Performance Portability and Core Utilities

  • Performance Portability
    Tools for enabling efficient computation across diverse hardware architectures, including CPUs, GPUs, and emerging HPC systems. Capabilities include abstractions for parallel execution, memory spaces, and hierarchical parallelism. Support for expressing parallel computations at multiple levels, including thread, team, and vector levels, ensuring efficient utilization of hardware resources. Abstractions for memory management, including multidimensional arrays with customizable memory layouts and traits for optimized data access patterns. Provided by package: Kokkos

  • Mathematical Kernels for Node-Local Computations
    Performance-portable implementations of mathematical kernels for dense and sparse linear algebra, graph algorithms, and batched computations. Capabilities include optimized sparse matrix operations, efficient BLAS routines, graph-based computations, and integration with vendor-optimized libraries. Thread-safe and asynchronous implementations ensure efficient concurrent execution and scalability. Provided by package: Kokkos Kernels

  • Distributed-Memory Linear Algebra
    Scalable infrastructure for distributed-memory computations, providing linear algebra objects such as sparse matrices, dense vectors, and graphs. Supports efficient parallel operations using MPI-based communication, including sparse matrix-vector multiplication, matrix-matrix multiplication, and graph-based operations. Features include data redistribution, halo exchange, and flexible templated objects for compatibility with diverse applications and architectures. Essential for large-scale simulations on leadership-class systems. Provided by package: Tpetra

  • Utility and Helper Tools
    Collection of tools for memory management, parameter lists, templated wrappers for BLAS/LAPACK, and XML parsing. These utilities simplify programming tasks and ensure consistent coding practices. Provided by package: Teuchos

Linear Solvers

  • Iterative Linear Solvers
    Comprehensive suite of iterative solvers for linear systems, including Krylov methods such as CG, GMRES, MINRES, and BiCGStab. These solvers support block and pseudo-block methods for solving systems with multiple right-hand sides, as well as advanced techniques like flexible GMRES and pipelined CG. Provided by package: Belos

  • Direct Linear Solvers
    Direct solvers for sparse linear systems, including interfaces to third-party solvers and node-local solvers optimized for shared-memory architectures. These solvers are essential for problems requiring robust and accurate solutions, such as circuit simulations and mechanics applications. Provided by package: Amesos2, ShyLU, Adelus

  • Large-Scale Eigenvalue Algorithms
    Framework for solving large-scale eigenvalue problems, including methods such as block Davidson, Krylov-Schur, locally optimal block preconditioned conjugate gradient (LOBPCG), and trace minimization. These algorithms are designed to handle large, sparse matrices arising in scientific and engineering applications, providing flexibility and scalability for diverse use cases. Provided by package: Anasazi

Preconditioners

  • One-Level Domain Decomposition
    Overlapping additive Schwarz methods for preconditioning, with options for local subdomain solves such as incomplete LU factorizations and direct solvers. These methods accelerate iterative solvers and include classic iterative techniques like Jacobi, Gauss-Seidel, and Chebyshev iterations, optimized for shared-memory architectures. Provided by package: Ifpack2

  • Multilevel Domain Decomposition
    Multilevel Schwarz preconditioners that emphasize scalability and robustness across challenging problems. These preconditioners support extension-based coarse spaces and are designed for algebraic construction, relying solely on the sparsity pattern of the system matrix. They have demonstrated scalability to hundreds of thousands of cores on supercomputers. Provided by package: FROSch

  • Multigrid Methods
    Scalable multigrid solvers for a wide range of PDEs, including Poisson-like operators, elasticity, convection-diffusion, and Maxwell’s equations. These solvers include aggregation-based algebraic multigrid methods, semi-coarsening for structured grids, and specialized solvers for multiphysics problems. Provided by package: MueLu

  • Physics-Based Block Preconditioners
    Block preconditioning strategies for multiphysics problems, leveraging the block structure of matrices to create efficient solvers. Strategies include block LU factorizations, SIMPLEC, LSC, and PCD preconditioners, with flexibility for defining custom inverse approximations for Schur complements. Provided by package: Teko

Discretization Utilities

  • Finite Element Local Assembly
    Tools for local assembly of finite element matrices and vectors, supporting high-order compatible discretizations for function spaces such as H(grad), H(curl), H(div), and L2. Capabilities include geometric operations, basis functions, orientation tools, and projection methods for efficient finite element computations. Provided by package: Intrepid2

  • Finite Element Assembly for Multiphysics Systems
    Tools for efficient finite element assembly, supporting mixed bases, multiphysics systems, and high-order discretizations. Capabilities include dependency management, distributed assembly, and support for block or fully coupled systems. Integrated with automatic differentiation for Jacobians and sensitivities, enabling scalable simulations and optimization. Provided by package: Panzer

  • Field Evaluation and Dependency Management
    Graph-based design for managing dependencies in PDE assembly, enabling rapid prototyping and integration of automatic differentiation tools. These capabilities support efficient evaluation of fields and derivatives, automating the computation of Jacobians, sensitivities, and other quantities required for nonlinear solvers and optimization. Provided by package: Phalanx

  • Meshless Approximation of Linear Operators
    Tools for meshless approximation of linear operators using generalized moving least squares (GMLS). These capabilities support applications such as data transfer and meshless discretization of PDEs, leveraging hierarchical parallelism for performance portability. Provided by package: Compadre

Nonlinear, Transient, and Optimization Solvers

  • Nonlinear Solvers
    Algorithms for solving nonlinear equations, including Newton-based methods, line search, trust region, and homotopy techniques. These solvers support Jacobian-free Newton-Krylov variants and provide robust options for handling large-scale nonlinear systems. Provided by package: NOX

  • Continuation and Stability Analysis
    Techniques for tracking solution families and investigating stability, including pseudo-arclength continuation, bifurcation tracking, and eigenvalue analysis. These capabilities are widely used in applications such as fluid dynamics and chemical reactor design. Provided by package: LOCA

  • Transient Solvers
    Framework for time integration, supporting explicit and implicit methods for first- and second-order ODEs. Capabilities include error control, sensitivity analysis, and transient optimization, making them suitable for simulations ranging from small systems to exascale computing. Provided by package: Tempus

  • Optimization Solvers
    State-of-the-art algorithms for constrained and unconstrained optimization, including trust-region methods, stochastic optimization, and nonsmooth optimization. These solvers support matrix-free computations and integrate seamlessly with PDE models for efficient optimization. Provided by package: ROL

Automatic Differentiation

  • Forward and Reverse Mode AD
    Tools for automatic differentiation using operator overloading, enabling efficient computation of derivatives for complex models. These capabilities integrate with performance-portable architectures, making them suitable for GPU-based systems and large-scale applications. Provided by package: Sacado

Uncertainty Quantification

  • Uncertainty Quantification and Stochastic Methods
    Tools for intrusive uncertainty quantification methods, including stochastic Galerkin projections and embedded ensemble propagation. Capabilities include efficient computation of polynomial chaos expansions, block-structured linear systems, and scalable ensemble-based simulations. Optimized for performance on modern architectures, enabling uncertainty propagation in large-scale multiphysics systems. Provided by package: Stokhos

Partitioning and Load Balancing

  • Partitioning and Load Balancing
    Tools for efficiently partitioning and distributing data objects such as sparse matrices across processors, ensuring balanced computational loads and minimizing communication overhead. These capabilities include support for hybrid parallelism and advanced algorithms like geometric partitioning, spectral graph partitioning, graph coloring, and MPI task placement. Provided by package: Zoltan, Zoltan

Mesh and Geometry Tools

  • Mesh Generation
    Tools for generating meshes for computational simulations, including structured, unstructured, and hybrid meshes. These capabilities support the creation of meshes for complex geometries and multiphysics applications. Provided by package: PAMGEN

  • Mesh Manipulation
    Utilities for modifying meshes, including operations such as mesh refinement, coarsening, and partitioning. These tools allow users to adapt meshes to specific simulation requirements or improve computational efficiency. Provided by package: SEACAS, STK, Percept

  • Mesh I/O
    Support for reading and writing mesh data in various formats, including Exodus, NetCDF, and other widely used formats in scientific computing. These capabilities enable interoperability with external mesh generation and visualization tools. Integration with visualization tools for inspecting and analyzing mesh structures and simulation results. These capabilities include support for exporting data to visualization software such as ParaView and VisIt. Provided by package: SEACAS, STK

  • Cell Topology
    Tools for defining and querying cell topology, including support for triangles, quadrilaterals, tetrahedrons, hexahedrons, wedges, and pyramids. These capabilities are essential for finite element and finite volume discretizations. Provided by package: Shards

  • Level-Set Methods
    Capabilities for handling level-set representations of geometries, enabling simulations involving moving boundaries, interfaces, and topological changes. These methods are particularly useful for fluid-structure interaction and multiphase flow problems. Provided by package: Krino

  • Mesh Refinement and Adaptivity
    Tools for refining and adapting meshes based on simulation results, including error indicators and solution gradients. These capabilities ensure accurate and efficient simulations by dynamically adjusting the mesh resolution. Provided by package: STK

  • Mesh Quality Assessment
    Utilities for assessing and improving mesh quality, including metrics for element shape, size, and aspect ratio. These tools help ensure that meshes are suitable for high-fidelity simulations. Provided by package: SEACAS, Percept

  • Mesh-Based Data Transfer
    Support for transferring data between meshes, including interpolation and projection methods for scalar, vector, and tensor fields. These capabilities are critical for multiphysics simulations and coupling between different models.
    Provided by package: SEACAS, STK

Interfaces and Adapters

  • Unified Solver Interface
    Cohesive interface to linear solvers and preconditioners, enabling runtime configuration through parameter lists. This interface simplifies solver management for complex applications and supports integration with multiple linear algebra backends. Provided by package: Stratimikos

  • Python Wrappers
    Python interfaces for selected capabilities, enabling rapid prototyping and algorithm development. These wrappers provide access to linear algebra, solvers, and preconditioners for efficient experimentation and integration. Provided by package: PyTrilinos2

  • Abstract Numerical Algorithms
    Interfaces for implementing high-level abstract numerical algorithms, enabling separation of algorithm development from linear algebra implementation. These abstractions support efficient reuse across multiple applications. Provided by package: Thyra

Trilinos continues to evolve, providing cutting-edge tools for scientific computing while maintaining performance portability across diverse hardware architectures.

Trilinos Packages

Trilinos Packages by Area