PNNL-13501 - Pacific Northwest National Laboratory

Figure 5a. OSO volume rendering of a 1240 atom portion of
the protein with empirical formula C382H632N115O106S5.
This macromolecule will be used for charge density
distribution modeling by Tjerk Straatsma. This work
requires extremely fast Poisson solves on minimal surfaces.
Figure 5b. The adaptive average Laplacian surface
enclosing the 1240 atom macromolecule built using NWGrid
and NWPhys. This is a minimal surface with the property
that the local average curvature of any point on the surface
grid is nearly flat relative to its nearest neighbor points. The
surface has the minimal surface area to enclosed volume
ratio.
The TRUEGRID package (XYZ Scientific Applications,
Inc., Livermore, California) for generating structured
grids. Each of these codes contains full-physics
capability and is quite complex, so that we continue to
invest extensive efforts toward learning to run these
codes.
We have models in development of SST S-SX embedded
with single-shell tanks, a 1240 atom biomolecule, two ion
trap experiments designed by Dr. Steven Barlow (EMSL),
and a local atmospheric flow through a mountain ravine
in New Mexico. We also have demonstrated that these
grid technologies may be used in molecular modeling
studies, for example, protein folding, and in systematic
extension of hydrodynamics to the molecular scale.
The computational applied mathematics that underlies the
areas of reactive transport and computational chemistry
includes PDEs, stochastic analysis, and numerical
methods. These applications require the fast and accurate
solution of quasi-linear and nonlinear PDEs derived from
equilibrium and nonequilibrium phenomena that are
formulated as coupled dynamical systems composed of
reaction-diffusion equations. In terms of mathematical
techniques, the difficulties lie in the development of
methods to manipulate discontinuous functions and
derivatives, as well as multidimensional singularities and
couplings. Many of the mathematical challenges in
solving these problems have a common origin in the
inherent geometry of the physics, and include highly
oscillatory coefficients, steep gradients, or extreme
curvatures at the moving and mixing shock fronts at
interfaces that are singular analytically.
To simulate the physical process more accurately, new
mathematical formulations of the physical problem, its
inherent geometry, its boundary conditions and solution
techniques, such as that developed previously by us, were
developed in conjunction with applications, grids, and
algorithmic and computational implementations. We
continued this work in FY 2000, with increasing emphasis
on geometrically faithful gridding, and plan to initiate an
investigation of stochastic grids. In FY 2000, we hired
Dr. Harold E. Trease and established NWGrid and
NWPhys as the flagship codes for the Applied
Mathematics Group within Theory, Modeling and
Simulation at EMSL.
Summary and Conclusions
It is our intention to identify and analyze the inherent
assumptions in each model and analyze the ramifications
of those assumptions on the appropriateness of the
presently used solution techniques, as well as the
constraints that they impose on the integration process of
the information generated/shared by the multiscale
physical chemistry models. It is our belief that when the
invariant geometry of a problem is captured and
maintained throughout an analysis, the greatest fidelity of
the results will be achieved and the physical mechanisms
of information transport across temporal and spatial scales
will be revealed. Our focus is on capturing the relevant
physics/chemistry—selection of the particular numerical
solution scheme is to be based in the inherent geometric
constraints of the problem to ensure preservation of
invariants. Subsequently, we will begin to unify the
models via a mid-scale model that will capture the
fundamental physics and chemistry of the problem of
interest.
Computational Science and Engineering 115