The Center for Efficient Exascale Discretizations has developed innovative mathematical algorithms for the DOE’s next generation of supercomputers.

# Topic: *PDE Methods*

The open-source MFEM library enables application scientists to quickly prototype parallel physics application codes based on PDEs discretized with high-order finite elements.

A high-fidelity, specialized code solves partial differential equations for plasma simulations.

The second annual MFEM workshop brought together the project’s global user and developer community for technical talks, Q&A, and more.

The MFEM software library provides high-order mathematical algorithms for large-scale scientific simulations. An October workshop brought together MFEM’s global user and developer community for the first time.

An LLNL mathematician and collaborators have developed a machine learning–based technique capable of deriving a mathematical model for the motion of binary black holes from gravitational wave data.

Our researchers will be well represented at the virtual SIAM Conference on Computational Science and Engineering (CSE21) on March 1–5. SIAM is the Society for Industrial and Applied Mathematics with an international community of more than 14,500 individual members.

Lawrence Livermore National Lab has named Stefanie Guenther as Computing’s fourth Sidney Fernbach Postdoctoral Fellow in the Computing Sciences. This highly competitive fellowship is named after LLNL’s former Director of Computation and is awarded to exceptional candidates who demonstrate the potential for significant achievements in computational mathematics, computer science, data science, or scientific computing.

Highlights include debris and shrapnel modeling at NIF, scalable algorithms for complex engineering systems, magnetic fusion simulation, and data placement optimization on GPUs.

Highlights include the latest work with RAJA, the Exascale Computing Project, algebraic multigrid preconditioners, and OpenMP.

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

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.

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