The Enabling Technologies for High-Order Simulations (ETHOS) project performs research of fundamental mathematical technologies for next-generation high-order simulations algorithms.

# Topic: *Discrete Mathematics*

The latest issue of LLNL's *Science & Technology Review* magazine showcases Computing in the cover story alongside a commentary by Bruce Hendrickson.

Highlights include scalable deep learning, high-order finite elements, data race detection, and reduced order models.

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.

Proxy apps serve as specific targets for testing and simulation without the time, effort, and expertise that porting or changing most production codes would require.

The SAMRAI library is the code base in CASC for exploring application, numerical, parallel computing, and software issues associated with structured adaptive mesh refinement.

This summer, the Computing Scholar Program welcomed 160 undergraduate and graduate students into virtual internships. The Lab’s open-source community was already primed for student participation.

This video describes MFEM (Modular Finite Element Methods), an open-source software library that provides advanced mathematical algorithms for use by scientific applications.

The Center for Efficient Exascale Discretizations recently released MFEM v4.1, which introduces features important for the nation’s first exascale supercomputers. LLNL's Tzanio Kolev explains.

Highlights include response to the COVID-19 pandemic, high-order matrix-free algorithms, and managing memory spaces.

The Center for Efficient Exascale Discretizations (CEED) within the ECP involves more than 30 computational scientists from 2 DOE labs (Livermore and Argonne) and 5 universities.

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

LLNL has named Will Pazner as Computation’s third Sidney Fernbach Postdoctoral Fellow in the Computing Sciences.

Highlights include complex simulation codes, uncertainty quantification, discrete event simulation, and the Unify file system.

Highlights include recent LDRD projects, Livermore Tomography Tools, our work with the open-source software community, fault recovery, and CEED.

Highlights include Computation’s annual external review, machine learning for ALE simulations, CFD modeling for low-carbon solutions, seismic modeling, and an in-line floating point compression tool.

The Extreme Resilient Discretization project (ExReDi) was established to address these challenges for algorithms common for fluid and plasma simulations.

GLVis is a lightweight OpenGL-based tool for accurate and flexible finite element visualization. It is based on MFEM, a finite element library developed at LLNL. GLVis provides interactive visualizations of general finite element meshes and solutions, both in serial and in parallel. It encodes a large amount of parallel finite element domain-specific knowledge; e.g., it allows the user to view parallel meshes as one piece, but it also gives them the ability to isolate each component and observe it individually. It provides support for arbitrary high-order and NURBS meshes (NURBS allow more accurate geometric representation) and accepts multiple socket connections so that the user may have multiple fully-functional visualizations open at one time. GLVis can also run a batch sequence, or a series of commands, which gives the user precise control over visualizations and enables them to easily generate animations.

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

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

The Serpentine project develops advanced finite difference methods for solving hyperbolic wave propagation problems. Our approach is based on solving the governing equations in second order differential formulation using difference operators that satisfy the summation by parts principle.

Through research funded at LLNL, scientists have developed BLAST, a high-order finite element hydrodynamics research code that improves the accuracy of simulations, provides a path to extreme parallel computing and exascale architectures, and gives an HPC advantage.