Mathematics Group

Multiphysics in Materials and Industrial Devices

The Voronoi Implicit Interface Method (VIIM) built by CRD Math researchers can track multiple coupled interfaces moving under complex physics constraints.

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Simulation of Vertical-Axis Wind Turbines

Optimizing blade design and structure in these unusual turbines is highly challenging. We were able to accurately compute optimal VAWT configurations in various environments.

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Rolling Tires and Failure

The process of fracture in tires is a complex problem in polymer chemistry, materials science, and mechanics. In order to effectively predict the state of balance for design purposes, one needs a meth…

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Implicit Sampling

The need to sample complicated many-dimensional probability densities arises in applications ranging from data analysis to computational physics.

About the Group

The Mathematics Group at LBNL develops new mathematical models, devises new algorithms, explores new applications, exports key technologies, and trains young scientists in support of DOE. We use mathematical tools from a variety of areas in mathematics, physics, statistics, and computer science, including statistical physics, differential geometry, asymptotics, graph theory, partial differential equations, discrete mathematics, and combinatorics. The problems we attack are both technologically interesting and mathematically challenging, and form a set of interrelated computing methodologies and applications in support of the DOE energy mission. »More about our mission and research.

Group Leader: James Sethian

Research Highlights

New Materials Design

Working jointly with the Berkeley Lab EFRC (Energy Frontier Research Center), we are developing novel techniques to prune detailed zeolite databases for potential materials for carbon sequestration.

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Granular Flow: Coal Hoppers and Pebble Bed Reactors

Together with Sandia National Lab, we have built large-scale simulations of an experimental pebble-bed nuclear reactor design, featuring 440,000 6 cm spherical particles that are slowly cycled through a cylindrical container, to analyze particle mixing between fuel and moderator

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High-Throughput Data Extraction from the DOE Advanced Light Source

We have built fast, automatic algorithms to extract data from synchrotron light sources. These methods, which combine PDE-based image segmentation with statistical methods, assembled 2D data slices in 3D, and extract relevant structures.

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Seismic imaging: Reconstruction of the earth from surface recordings

We have been able to build fast and robust algorithms to (i) convert time migrated coordinates to depth coordinates and (ii) convert migration velocities to depth velocities. These algorithms allowed imaging of subsurface substructures 3.3 km deep in a North Sea salt dome example with severe lateral variations.

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Assimilating ocean and geophysics data

Our work on implicit sampling makes it possible to produce sample states that have a consistently high probability, reducing by a large factor the exploratory computing that needs to be done to eliminate unlikely possibilities.