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Mathematics Group
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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.


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.


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...


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


Grain Boundaries and Stresses: Microchip Component Failure and Electromigration

We developed a continuum model of mass transport phenomena in microelectronic circuits due to high current densities (electromigration) and gradients in normal stress along grain boundaries.

Fluid Pinch-off and Sprays

We have built a new mathematical model applicable to a host of fluid breakage issues. Our new approach relies on embedding the interface, the velocity, and the potential in higher dimensional implicit forms, and then solving a coupled set of PDEs that naturally transition through fluid breakup

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.
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Curved Meshing for Fixed and Deforming Boundaries Using Elasticity

We have applied our new methodology for building curved unstructured meshes on fixed and deforming boundaries, using an elasticity formulation, on a collection of coupled interacting fluid/solid body problems. These include meshing of moving wings in unmanned aerial vehicles.
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Modeling of Industrial Printing and Nano-Jetting Spray Delivery

We built a computational environment to model two-phase microjetting in manufacturing and industrial devices.

More from Research Highlights »