Discretizations & Methods

Much of our physical world can be described by mathematics, but only the simplest mathematical equations can be solved with pencil and paper. To take advantage of computers, we must translate mathematical equations into a form that computers can manipulate. At Berkeley Lab, we develop new discretizations to represent complex systems, as well as new methods to solve discretized equations.

Our applied mathematicians work with domain scientists to develop state-of-the-art algorithms and methods for finite volume and discontinuous Galerkin schemes, level set methods and cut cell methods for modeling interfaces, specialized methods for stochastic differential equations, particle and particle-mesh algorithms such as Particle-in-Cell (PIC) and Particle-Particle-Particle-Mesh (PPPM), graph and combinatorial algorithms, discrete event simulation, adaptive mesh refinement and a broad range of approaches for coupling algorithms with different physics at different scales.

Projects

Algoim

Algoim is a collection of high-order accurate numerical methods and C++ algorithms for working with implicitly-defined geometry and level set methods. Contact: Robert Saye (Saye on the Web)

Adaptive Mesh Refinement Frameworks

AMReX and Chombo are software frameworks that support development of applications that use block-structured adaptive mesh refinement. Both support particle and particle-mesh data structures and algorithms as well as calculations in complex geometries using an embedded boundary/cut cell approach. AMReX enables users to use GPU-accelerated hardware based on CUDA, HIP and DPC++. AMReX Contact: Ann Almgren, Chombo Contact: Daniel Martin

Machine Learning Accelerated Models

Our Machine Learning Development Team is using machine learning models within an AMReX framework to accelerate the time-to-solution of computational kernels without reducing accuracy. Contact: Andy Nonaka (Nonaka on the Web)

PFASST (Parallel Full Approximation Scheme in Space and Time)

PFASST is an algorithm designed to provide parallelism in the time direction for the numerical solution of ordinary and partial differential equations. Contact: Xiaoye Sherry Li (Li on the Web)

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