## Design of new daspk for sensitivity analysis (1999)

Citations: | 23 - 8 self |

### BibTeX

@TECHREPORT{Li99designof,

author = {Shengtai Li and Linda Petzold},

title = {Design of new daspk for sensitivity analysis},

institution = {},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

A new version of DASPK, DASPK3.0, with capability for sensitivity analysis is pre-sented in this report. DASPK3.0 differs from the sensitivity code DASPKSO, described in [12], in several ways. DASPK3.0 has all the features, which were not available in DASPKSO, of the previous version DASPK2.0. One of these features is an improved algorithm for calculation of consistent initial conditions for index-zero or index-one systems. DASPK3.0 also incorporates a mechanism for initialization and solution of index-2 systems. Other improvements in DASPK3.0 include a more accurate error and convergence test, particularly for the sensitivity analysis. We implemented the Krylov method for sensitivity computation with a different strategy from DASPKSO, and made it more efficient and easier for parallel computing. We also added the staggered correc-tor method [7] for both the direct and Krylov method. We implemented the sensitivity analysis with an internal parallel mode, which is easy to use for both serial and parallel computation with message passing interface (MPI). We also incorporated automatic dif-ferentiation into DASPK3.0 to evaluate the Jacobian matrix and sensitivity equations. The goal of our design has been to be compatible as much as possible with DASPK2.0, to minimize memory and storage requirements for sensitivity analysis, and to speed up the computation for a large number of sensitivity parameters.

### Citations

1462 | A generalized minimal residual algorithm for solving nonsymmetric linear systems
- Saad, Schultz
- 1986
(Show Context)
Citation Context ...ct linear system methods. In DASPK, the linear systems that arise at each time step are solved with either direct linear system methods, or with a preconditioned Krylov iterative method, namely GMRES =-=[16]-=-. For large-scale systems, the iterative method combined with a suitable preconditioner can be quite effective. Sensitivity analysis of DAEs is important in many engineering and scientific application... |

1117 |
Using MPI: Portable Parallel Programming With the Message-Passing Interface
- Gropp, Lusk, et al.
- 1994
(Show Context)
Citation Context ...rgonne National Laboratory and Mississippi State University [6]. Programs written with MPI are portable between different machines. A tutorial on how to use MPI to write parallel programs is given in =-=[9]-=-. The MPI packages, including the library and running examples, can be freely downloaded from http://www.mcs.anl.gov/mpi We assume here that the reader has a basic knowledge of MPI. When MPI starts, i... |

374 | SNOPT: An SQP algorithm for large-scale constrained optimization - Gill, Murray, et al. - 2002 |

157 | ADIFOR Generating Derivative Codes from FORTRAN Programs
- Bischof, Carle, et al.
- 1992
(Show Context)
Citation Context ...or the sensitivities. For some strongly nonlinear problems, exact input of the Jacobian in the direct method can greatly improve the accuracy and efficiency. The automatic differentiation tool ADIFOR =-=[1]-=- can generate a subroutine to compute the Jacobian matrix with accuracy up to round-off error. In our experience, ADIFOR-generated derivative code usually outperforms divided-difference approximations... |

127 | A description of dassl: A differential/algebraic system solver. technical report 8637, Sandia National Laboratories - Petzold - 1982 |

59 |
Using Krylov methods in the solution of large-scale differential-algebraic systems
- Brown, Hindmarsh, et al.
- 1994
(Show Context)
Citation Context ... (1) where F , y, and y ′ are N-dimensional vectors. Two software packages have been written for solving initial value problems for the DAE system (1) —DASSL [13], and an extension of it called DASPK =-=[3]-=-. Both use variable-order variable-stepsize backward differentiation formulas. DASSL solves the linear systems that arise at each time step by dense or banded direct linear system methods. In DASPK, t... |

51 | Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution
- Cao, Li, et al.
(Show Context)
Citation Context ...lementation often fails when the matrix J is ill-conditioned. This is because the right-hand side of equation (32) can be very large and can introduce large round-off errors when J is ill-conditioned =-=[11]-=-. In DASPK3.0, the following linear system is solved for the sensitivities: Jδ = Js (0) i + (n+1) ∂F ∂y ′ β + n+1 ∂F , (33) ∂pi where δ = s (0) i (n+1) − si (n+1) . The right-hand side of (33) is easy... |

36 |
A Model Implementation of MPI
- Doss, Gropp, et al.
- 1993
(Show Context)
Citation Context ... involving the MPI library, for use with serial computation How to use DASPK with parallel computation MPI was developed by researchers at Argonne National Laboratory and Mississippi State University =-=[6]-=-. Programs written with MPI are portable between different machines. A tutorial on how to use MPI to write parallel programs is given in [9]. The MPI packages, including the library and running exampl... |

30 |
Efficient sensitivity analysis of large-scale differential–algebraic systems
- Feehery, Tolsma, et al.
- 1997
(Show Context)
Citation Context ...mented the Krylov method for sensitivity computation with a different strategy from DASPKSO, and made it more efficient and easier for parallel computing. We also added the staggered corrector method =-=[7]-=- for both the direct and Krylov method. We implemented the sensitivity analysis with an internal parallel mode, which is easy to use for both serial and parallel computation with message passing inter... |

27 | Numerical methods and software for sensitivity analysis of differential-algebraic systems
- Maly, Petzold
- 1996
(Show Context)
Citation Context ... Li and Linda Petzold Abstract A new version of DASPK, DASPK3.0, with capability for sensitivity analysis is presented in this report. DASPK3.0 differs from the sensitivity code DASPKSO, described in =-=[12]-=-, in several ways. DASPK3.0 has all the features, which were not available in DASPKSO, of the previous version DASPK2.0. One of these features is an improved algorithm for calculation of consistent in... |

24 |
Sensitivity analysis of initial value problems with mixed ODEs and algebraic equations
- Caracotsios, Stewart
- 1985
(Show Context)
Citation Context ...e can be sharply reduced by the matrix times vector method. 5.3 Implementation of staggered direct method The staggered direct method has been implemented in the DASAC code by Caracotsios and Stewart =-=[5]-=-. In DASAC, system (8) is transformed into Jsi (n+1) = � − ∂F ∂y ′ β − n+1 ∂F � ∂pi , (32) where βi = s ′(0) i (n+1) − αs (0) i (n+1) . To solve a linear system in this way requires extra storage for ... |

15 | Numerical optimal control of parabolic PDEs using DASOPT
- Petzold, Rosen, et al.
- 1997
(Show Context)
Citation Context ...re a gradient and Jacobian matrix which are derivatives of the objective function and of the constraints with respect to the optimization variables. DASPKSO has been used to compute these derivatives =-=[14]-=-. One of the difficulties for the optimization problems is that the solution output from the optimizer does not satisfy the consistent initial conditions required by DASPK. The consistent initial cond... |

14 | Consistent Initial Condition Calculation for Differential-Algebraic Systems
- Brown, Hindmarsh, et al.
- 1998
(Show Context)
Citation Context ...rrector step. This implementation is called the simultaneous corrector method. Since the DASPKSO code was designed based on the first version, DASPK1.0, of DASPK, it did not include the new mechanism =-=[4]-=- to calculate consistent initial conditions for index-0 or 1 DAEs. We rewrote it and incorporated the features of the newer version, DASPK2.0, of DASPK. The Krylov method in DASPKSO solves a large lin... |

10 | A description of DASSL: A di erential/algebraic system solver, in: R.S. Stepleman, et al - Petzold - 1983 |

6 |
Consistent initial condition calculation for di®erential-algebraic systems
- Brown, Hindmarsh, et al.
- 1998
(Show Context)
Citation Context ...corrector step. This implementation is called the simultaneous corrector method. Since the DASPKSO code was designed based on thesrst version, DASPK1.0, of DASPK, it did not include the new mechanism =-=[4]-=- to calculate consistent initial conditions for index-0 or 1 DAEs. We rewrote it and incorporated the features of the newer version, DASPK2.0, of DASPK. The Krylov method in DASPKSO solves a large lin... |

6 |
E±cient Sensitivity Analysis of Large-Scale Di®erential-Algebraic Systems
- Feehery, Tolsma, et al.
- 1997
(Show Context)
Citation Context ...mplemented the Krylov method for sensitivity computation with a dierent strategy from DASPKSO, and made it more ecient and easier for parallel computing. We also added the staggered corrector method [=-=7]-=- for both the direct and Krylov method. We implemented the sensitivity analysis with an internal parallel mode, which is easy to use for both serial and parallel computation with message passing inter... |

5 |
private communication
- Hindmarsh
- 2003
(Show Context)
Citation Context ...o nearly equal numbers. It is also hard to select a δi that is appropriate for all the variables for a badly scaled problem, because y, y ′ and p may have different scalings. Recently, Alan Hindmarsh =-=[10]-=- proposed a different method to select the increment δi for equation (11). In [12], where ∆ is a scale factor, and δi = ∆ max(|pi|, ||vi||2) (12) vi = � W T j /W T iny+j � : j = 1, ..., ny . The probl... |

5 |
Adjoint Sensitivity Analysis for Di®erential-Algebraic Equations: The Adjoint DAE System and its Numerical Solution
- Cao, Li, et al.
- 2003
(Show Context)
Citation Context ...plementation often fails when the matrix J is ill-conditioned. This is because the right-hand side of equation (32) can be very large and can introduce large round-o errors when J is ill-conditioned [=-=11]-=-. In DASPK3.0, the following linear system is solved for the sensitivities: J = Js (0) i (n+1) + @F @y 0 n+1s+ @F @p i ; (33) wheres= s (0) i (n+1) s i (n+1) . The right-hand side of (33) is easy to o... |

1 |
Parallel sensitivity analysis for DAEs with many parameters, submitted to Concurrency: Practice and Experience
- Petzold, Zhu
- 1998
(Show Context)
Citation Context ... Each sensitivity is independent of the others in sensitivity analysis, which is ideal for parallel computation. Several parallel implementations for the sensitivity analysis of DAEs were compared in =-=[15]-=-. The distributed parameter only (DPO) method proved to be the most efficient one in [15]. However, the DPO method as implemented in [15] requires the user to distribute the parameters to each process... |