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- Yang Cao, Shengtai Li, Linda R. Petzold, Radu Serban
- SIAM J. Scientific Computing
- 2003

An adjoint sensitivity method is presented for parameter-dependent differentialalgebraic equation systems (DAEs). The adjoint system is derived, along with conditions for its consistent initialization, for DAEs of index up to two (Hessenberg). For stable linear DAEs, stability of the adjoint system (for semi-explicit DAEs) or of an augmented adjoint system… (More)

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… (More)

Sensitivity analysis for DAE systems is important in many engineering and scienti c applications. The information contained in the sensitivity trajectories is useful for parameter estimation, optimization, model reduction and experimental design. In this paper we present algorithms and software for sensitivity analysis of large-scale DAE systems of index up… (More)

- Shengtai Li, Linda R. Petzold, Yuhe Ren
- SIAM J. Scientific Computing
- 1998

Moving mesh methods based on the equidistribution principle (EP) are studied from the viewpoint of stability of the moving mesh system of differential equations. For fine spatial grids, the moving mesh system inherits the stability of the original discretized partial differential equation (PDE). Unfortunately, for some PDEs the moving mesh methods require… (More)

This paper extends a class of approximate Riemann solvers devised by Harten, Lax and van Leer (HLL) for Euler equations of hydrodynamics to magneto-hydrodynamics (MHD) equations. In particular, we extend the two-state HLLC (HLL for contact wave) construction of Toro, Spruce and Speares to MHD equations. We derive a set of HLLC middle states that satisfies… (More)

An e4cient numerical method for sensitivity computation of large-scale di$erential-algebraic systems is developed based on the adjoint method. Issues that are critical for the implementation are addressed. Complexity analysis and numerical results demonstrate that the adjoint sensitivity method is advantageous over the forward sensitivity method for… (More)

A new adjoint sensitivity analysis approach is presented for time-dependent partial differential equations with adaptive mesh refinement. The new approach, called ADDA, combines the best features of both the adjoint of the discretization (AD) and discretization of the adjoint (DA) approaches. It removes the obstacles of applying AD to adaptive methods and,… (More)

- Shengtai Li
- J. Comput. Physics
- 2008

This paper extends the central finite-volume schemes of Liu et al. [Y. Liu, C.-W. Shu, E. Tadmor, M. Zhang, Non-oscillatory hierarchical reconstruction for central and finite-volume schemes, Commun. Comput. Phys. 2 (2007) 933–963] on overlapping cells to the magneto-hydrodynamic (MHD) equations. In particular, we propose a high order divergence-free… (More)

tion, which is often called a reaction–convection–diffusion equation, is representative of many problems which are It is well known that moving mesh and upwinding schemes are two kinds of techniques for tracking the shock or steep wave front solved by moving mesh methods in one dimension. in the solution of PDEs. It is expected that their combination should… (More)

In this paper, a high order finite difference weighted essentially non-oscillatory (WENO) scheme is combined with adaptive mesh refinement (AMR) to solve problems that require multi-resolution in space and time. Because conservative finite difference schemes of third or higher order of accuracy can only be achieved on uniform rectangular or smooth… (More)