Topic: Computational Math

Based on a discretization and time-stepping algorithm, these equations include a local order parameter, a quaternion representation of local orientation, and species composition.

This scalable first-principles MD algorithm with O(N) complexity and controllable accuracy is capable of simulating systems that were previously impossible with such accuracy.

GLVis is a lightweight tool for accurate and flexible finite element visualization that provides interactive visualizations of general FE meshes and solutions.

High-resolution finite volume methods are being developed for solving problems in complex phase space geometries, motivated by kinetic models of fusion plasmas.

Researchers are testing and enhancing a neutral particle transport code and its algorithm to ensure that they successfully scale to larger and more complex computing systems.

LLNL and University of Utah researchers have developed an advanced, intuitive method for analyzing and visualizing complex data sets.

These Fortran solvers tackle the initial value problem for ODE systems. The collection includes solvers for systems given in both explicit and linearly implicit forms.

The NSDE project is focused on research and development of nonlinear solvers and sensitivity analysis techniques for nonlinear, time-dependent, and steady-state partial differential equations.

The flourishing of simulation-based scientific discovery has also resulted in the emergence of the UQ discipline, which is essential for validating and verifying computer models.

These methods for solving hyperbolic wave propagation problems allow for complex geometries, realistic boundary and interface conditions, and arbitrary heterogeneous material properties.

A new algorithm for use with first-principles molecular dynamics codes enables the number of atoms simulated to be proportional to the number of processors available.

BLAST is a high-order finite element hydrodynamics research code that improves the accuracy of simulations and provides a path to extreme parallel computing and exascale architectures.

This project constructs coarse time grids and uses each solution to improve the next finer-scale solution, simultaneously updating a solution guess over the entire space-time domain.