Stokhos: Stochastic Galerkin Uncertainty Quantification Methods

Outline

• Introduction
• Third-Party Libraries
• Contacts

Introduction

Stokhos is a Trilinos package for applying intrusive stochastic Galerkin uncertainty quantification methods to nonlinear dynamical systems, primarily stochastic partial differential equations.

Stokhos provides several types of capabilities

• Classes defining families of univariate and multivariate orthogonal polynomials: Stokhos::OneDOrthogPolyBasis and Stokhos::OrthogPolyBasis.
• Classes defining quadrature methods for orthogonal polynomials: Stokhos::Quadrature.
• Classes for generating stochastic residual coefficients using automatic differentiation with Sacado: Stokhos::OrthogPolyExpansion
• Classes for forming and solving stochastic Galerkin linear systems: Stokhos::MatrixFreeEpetraOp and Stokhos::MeanEpetraOp.
• Classes for providing a nonlinear interface to nonlinear stochastic Galerkin problems: Stokhos::SGModelEvaluator.

Third-Party Libraries

In addition to the standard Trilinos third-party libraries of BLAS, LAPACK, and MPI, Stokhos can make use of two more: the fortran UQ Toolkit of Debusschere et al, and Dakota.

Fortran UQ Toolkit

To enable the fortran UQ toolkit, add -D TPL_ENABLE_ForUQTK=ON to your cmake configure arguments and specify the library path to your installation via -D ForUQTK_LIBRARY_DIRS. This activates the expansion class Stokhos::ForUQTKOrthogPolyExpansion for generating stochastic galerkin residual coefficients using either time integration or Taylor series calculations.

Dakota

Dakota support is provided through the Trilinos package TriKota and currently, requires the development version of Dakota available here. To enable Dakota support, unpack a recent Dakota tarball in Trilinos/packages/TriKota and then add -D Trilinos_ENABLE_TriKota:BOOL=ON to your configure arguments. This activates sparse-grid quadrature methods based on Smolyak algorithms through Stokhos::SparseGridQuadrature. See the TriKota package documentation for more information on building and using TriKota.

Contacts

Stokhos is primarily developed and maintained by Eric Phipps with significant contributions by Bert Debusschere, Omar Knio, Chris Miller, and Habib Najm.