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- Dana A. Knoll
- 2003

Jacobian-free Newton–Krylov (JFNK) methods are synergistic combinations of Newton-type methods for superlinearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations. The link between the two methods is the Jacobian-vector product, which may be probed approximately without forming and storing the… (More)

A Multigrid Newton–Krylov Method for Multimaterial Equilibrium Radiation Diffusion1 William J. Rider,∗ Dana A. Knoll,∗ and Gordon L. Olson† ∗Hydrodynamic Methods Group, Applied Theoretical and Computational Physics Division, Los Alamos National Laboratory, MS D413, Los Alamos, New Mexico 87545; and †Transport Methods Group, Applied Theoretical and… (More)

- Dana A. Knoll, L C Chacón
- Physical review letters
- 2006

The coalescence of magnetic islands in the low-resistivity eta, Hall-MHD regime is studied. The interaction between the ion inertial length d(i) and the dynamically evolving current sheet scale length deltaJ is established. Initially, d(i) << deltaJ. If eta is such that deltaJ dynamically thins down to d(i) prior to the well-known sloshing phenomena, then… (More)

- Dana A. Knoll, V. A. Mousseau, Luis Chacón, John A. Reisner
- J. Sci. Comput.
- 2005

Stiff wave systems are systems which exhibit a slow dynamical time scale while possessing fast wave phenomena. The physical effects of this fast wave may be important to the system, but resolving the fast time scale may not be required. When simulating such phenomena one would like to use time steps on the order of the dynamical scale for time integration.… (More)

- Dana A. Knoll, William J. Rider
- SIAM J. Scientific Computing
- 1999

- Dana A. Knoll, Paul R. McHugh
- SIAM J. Scientific Computing
- 1998

- Samet Y. Kadioglu, Dana A. Knoll
- J. Comput. Physics
- 2010

- Dana A. Knoll, W. B. VanderHeyden, V. A. Mousseau, Douglas B. Kothe
- SIAM J. Scientific Computing
- 2001

- Jeffrey Willert, C. T. Kelley, Dana A. Knoll, HyeongKae Park
- SIAM J. Scientific Computing
- 2013

In this paper we describe a hybrid deterministic/Monte Carlo algorithm for neutron transport simulation. The algorithm is based on nonlinear accelerators for source iteration, using Monte Carlo methods for the purely absorbing high-order problem and a Jacobian-free Newton– Krylov iteration for the low-order problem. We couple the Monte Carlo solution with… (More)

- Bradford G. Stone, Linda Larsen, Dana A. Knoll, Victor A. Bloomfield, William Duane
- The Journal of laboratory and clinical medicine
- 1992

Micelles and vesicles coexist in native bile. Mixed micelles are composed of bile salt, phospholipid, and cholesterol. Micellar bile salt is in equilibrium with the aqueous phase bile salt (intermicellar bile salt), and mixed micelles can be converted to cholesterol-phospholipid vesicles by depletion of bile salt. To determine the amount of cholesterol… (More)