Matrix-free methods for stiff systems of ODE's
SIAM Journal on Numerical Analysis
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
VODE: a variable-coefficient ODE solver
SIAM Journal on Scientific and Statistical Computing
Numerical methods and software for sensitivity analysis of differential-algebraic systems
Applied Numerical Mathematics
Efficient sensitivity analysis of large-scale differential-algebraic systems
Applied Numerical Mathematics
ADIC: an extensible automatic differentiation tool for ANSI-C
Software—Practice & Experience
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs
ACM Transactions on Mathematical Software (TOMS)
Sensitivity analysis of large-scale time dependent PDEs
Applied Numerical Mathematics
Automatic differentiation of algorithms
Numerical Modeling in Applied Physics and Astrophysics
Numerical Modeling in Applied Physics and Astrophysics
Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer
SIAM Journal on Scientific Computing
Adifor 2.0: Automatic Differentiation of Fortran 77 Programs
IEEE Computational Science & Engineering
Radiation diffusion for multi-fluid Eulerian hydrodynamics with adaptive mesh refinement
Journal of Computational Physics
Design of new Daspk for Sensitivity Analysis
Design of new Daspk for Sensitivity Analysis
New physics-based preconditioning of implicit methods for non-equilibrium radiation diffusion
Journal of Computational Physics
PVODE, an ODE Solver for Parallel Computers
International Journal of High Performance Computing Applications
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
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In this paper, we discuss the computation and use of solution sensitivities for analyzing radiation diffusion problems and the dependence of solutions on input parameters. The derivation of the sensitivity equations is given, along with a description of the method for solving them in tandem with the simulation. The parameter values express material opacity as a power-law of material temperature and density. The computed sensitivities reveal important qualitative details about the temperature coupling and diffusion processes. It is also shown that these sensitivities are valuable for ranking the parameters from most to least influential, designing improved experiments, and quantifying uncertainty in the simulation results. Lastly, the numerical examples show that these various types of sensitivity analysis are only moderately expensive to perform relative to solving the simulation by itself.