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

# Topic: *Discrete Mathematics*

Hosted at LLNL, the Center for Efficient Exascale Discretizations’ annual event featured breakout discussions, more than two dozen speakers, and an evening of bocce ball.

From wind tunnels and cardiovascular electrodes to the futuristic world of exascale computing, and with a few fantastic beasts thrown in for good measure, Brian Gunney has been finding solutions for unsolvable problems.

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

Open-source software has played a key role in paving the way for LLNL's ignition breakthrough, and will continue to help push the field forward.

UCLA's Institute for Pure & Applied Mathematics hosted LLNL's Tzanio Kolev for a talk about high-order finite element methods.

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

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

Highlights include MFEM community workshops, compiler co-design, HPC standards committees, and AI/ML for national security.

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

Researchers will address the challenge of efficiently differentiating large-scale applications for the DOE by building on advances in LLNL’s MFEM finite element library and MIT’s Enzyme AD tool.

Winning the best paper award at PacificVis 2022, a research team has developed a resolution-precision-adaptive representation technique that reduces mesh sizes, thereby reducing the memory and storage footprints of large scientific datasets.

This project advances research in physics-informed ML, invests in validated and explainable ML, creates an advanced data environment, builds ML expertise across the complex, and more.

The MAPP incorporates multiple software packages into one integrated code so that multiphysics simulation codes can perform at scale on present and future supercomputers.

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.

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.

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

Highlights include debris and 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 the 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.