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

# Topic: *Computational Math*

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.

CASC computational mathematician Andrew Gillette has always been drawn to mathematics and says it’s about more than just crunching numbers.

This issue highlights some of CASC’s contributions to making controlled laboratory fusion possible at the National Ignition Facility.

With simple mathematical modifications to a common model of clouds and turbulence, LLNL scientists and their collaborators helped minimize nonphysical results.

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.

Responding to a DOE grid optimization challenge, an LLNL-led team developed the mathematical, computational, and software components needed to solve problems of the real-world power grid.

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

An LLNL Distinguished Member of Technical Staff, Falgout is still finding the fun in problem solving as project leader for two of CASC’s most cutting-edge multigrid method computing projects, hypre and XBraid.

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.

libROM is a library designed to facilitate Proper Orthogonal Decomposition (POD) based Reduced Order Modeling (ROM).

The prestigious fellow designation is a lifetime honorific title and honors SIAM members who have made outstanding contributions to fields served by the organization.

A new component-wise reduced order modeling method enables high-fidelity lattice design optimization.

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

LLNL’s archives provide a glimpse into the career and contributions of a computing pioneer.

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.

An LLNL Distinguished Member of Technical Staff, Carol Woodward consults on a diverse array of projects at the Lab and beyond. “It’s nice because it means I can work at the same place and not just do one thing for a long time,” she says.

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.

The prestigious award is handed out every two years and recognizes outstanding contributions to the development and use of mathematical and computational tools and methods for the solution of science and engineering problems.

This project solves initial value problems for ODE systems, sensitivity analysis capabilities, additive Runge-Kutta methods, DAE systems, and nonlinear algebraic systems.

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.

The first article in a series about the Lab's stockpile stewardship mission highlights the roles of computer simulations and exascale computing.

The Advanced Technology Development and Mitigation program within the Exascale Computing Project shows that the best way to support the mission is through open collaboration and a sustainable software infrastructure.