Georg Stadler
New York University, NY·Mathematics & Statistics
Many problems in science and engineering are described by nonlinear equations, often partial differential equations (PDEs), which relate how quantities change across space and time. Computers usually solve them with Newton's method, which repeatedly replaces the hard problem with a simpler linear one.
- Fields
Mathematics & Statistics
Computer Science
Earth & Environmental Science
- Topics
nonlinear solvers
Newton's method
nonlinear preconditioning
- Grants
- 2 known grants, through Aug 2027
What they work on
- Develop lifted Newton methods that move severely nonlinear PDE systems into a higher-dimensional space and apply nonlinear transformations before linearization, a form of nonlinear preconditioning.
- Determine theoretically and through systematic study which classes of nonlinear PDE problems converge faster with lifted Newton preconditioning, and explain why.
- Develop solver adaptivity that uses equation residuals to focus computing on shifting, localized regions of large linear and nonlinear systems, implemented in the scalable finite element Stokes solver Rhea.
- Simulate coupled plate tectonics and great earthquakes, adding visco-elastic and frictional models in Rhea, first in 2D and 3D and then for Cascadia and northwestern Pacific subduction systems.
More about the research
Newton's method is fast near the answer but can stall or fail when started far away, and very large problems strain even supercomputers. The lab's two projects target these issues. One builds better general-purpose nonlinear solvers. The other develops solvers that shift computing effort where it is needed most, applied to how earthquakes relate to plate tectonics.
Why it matters
Great subduction-zone earthquakes are among the largest natural hazards for the United States and other countries. Models linking plate motion to earthquake stress could deepen understanding of where and when they occur, including in Cascadia. More reliable nonlinear solvers could also speed up parameter estimation, control and design problems across science and engineering.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Bo Dong
University of Massachusetts-Dartmouth, MA·Mathematics & Statistics
Analyze a new conservative discontinuous Galerkin (DG) method that preserves conserved quantities through implicit penalty parameters, applied to the Korteweg-de Vries equation for shallow-water waves.
Qingguo Hong
Missouri University of Science and Technology, MO·Mathematics & Statistics
Develop discretizations of multiple-network poroelastic (MPET) models that remain robust across parameter ranges, strongly conserve mass, and keep the stress tensor exactly symmetric.
John Naliboff
New Mexico Institute of Mining and Technology, NM·Earth & Environmental Science
Improve the performance and robustness of the linear and nonlinear solvers in ASPECT, the open-source code for simulating mantle convection and long-term tectonics, so complex models run with fewer computational resources.
The school
New York University: 72 labs on PI Pages, $1.5B a year on research, 540 research doctorates a year.
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