We’re developing algorithms and software to enable the scalable solution of equations central to large-scale science simulations. Our research involves developing new mathematics and computing techniques, with a major focus on methods (e.g., multilevel methods) suitable for the next generation of extreme-scale supercomputers. View content related to Solvers.
Overture is an object-oriented code framework for solving partial differential equations (PDEs). It provides a portable, flexible software development environment for applications that involve the simulation of physical processes in complex moving geometry . It is implemented as a collection of C++ libraries that enable the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture is designed for solving problems on a structured grid or a collection of structured grids. In particular, it can use curvilinear grids, adaptive mesh refinement, and the composite overlapping grid method to represent problems involving complex domains with moving components. We have also developed techniques for building grids on CAD geometries and for building hybrid grids that can be used with applications that use unstructured grids.
For 20 years, scientists from LLNL’s Center for Applied Scientific Computing (CASC) have contributed scientific research and development in mathematics, computer science, and data science that have directly impacted national security and advanced basic science.
SUNDIALS is a SUite of Nonlinear and DIfferential/ALgebraic equation Solvers. It consists of the following six solvers: CVODE, solves initial value problems for ordinary differential equation (ODE) systems; CVODES, solves ODE systems and includes sensitivity analysis capabilities (forward and adjoint); ARKODE, solves initial value ODE problems with additive Runge-Kutta methods, include support for IMEX methods; IDA, solves initial value problems for differential-algebraic equation (DAE) systems; IDAS, solves DAE systems and includes sensitivity analysis capabilities (forward and adjoint); KINSOL, solves nonlinear algebraic systems.
A new parallel-in-time method dramatically decreases solution time for various simulations.
CASC researcher Carol Woodward consults on a diverse array of projects at the Laboratory and beyond. “It’s nice because it means I can work at the same place and not be stuck just doing one thing,” she says.
Livermore’s hypre library of solvers makes larger, more detailed simulations possible by solving problems faster than ever before. It offers one of the most comprehensive suites of scalable parallel linear solvers available for large-scale scientific simulation.