Highly accurate and structure-preserving numerical methods for nonlinear partial differential equations

Organizers: Jorge E. Macías-Díaz  • Qin Sheng  • Joshua Lee Padgett

This page contains the details of the proposed Special Session at the Joint Mathematics Meeting to be held in Denver Colorado, January 15-18 2020 (see here). The organizers intend to add more details to this page—such as presentation titles, abstracts, and presentation slides—as they are obtained. Any questions or comments regarding this web page may be sent via this link.

This session will have two time slots. The first is Thursday, January 16, 2020, 1:00-4:00pm and the second is Friday, January 17, 2020, 8:00-11:00am.

Description: Structure-preserving methods have emerged as a central topic in computational mathematics. It has been realized that an integrator must be designed to preserve as many of the intrinsic features of the underlying problems as possible, such as conserving the mass, momentum and energy, as well as the symplecticity and multisymplecticity of physical systems. Structure-preserving algorithms can be effectively utilized for simulations of a variety of theoretical and application problems, ranging from celestial mechanics, quantum mechanics, fluid dynamics, and artificial intelligence.

This special session is dedicated to recent advances in the aforementioned efforts, with a focus on high accuracy and structure-preserving algorithms when partial differential equations are targeted. We intend to accommodate a sufficiently broad spectrum of investigations, and will consider both theoretical and computational aspects of the burgeoning field.

The schedule is below (with links to the abstract available, too).

Thursday, January 16 (1-4pm) [Room 102, Colorado Convention Center]

Ronald E. Mickens (NSFD Schemes: A methodology for constructing structure-preserving discretizations for differential equations). Presentation Slides
Jeonghun Lee (A hybridized discontinuous Galerkin method for the Stokes equations with symmetric tensor approximation).
Alexey Sukhinin (Propagation of light in multi-frequency moving focus model).
Julienne Kabre (A splitting approximation for the numerical solution of a self-adjoint quenching problem). Presentation Slides
Tiffany Nicole Jones (Solving highly oscillatory wave equations with an asymptotically stable dual-scale compact method).
Qin Sheng (A review and expectation of the numerical stabilities for nonlinear Kawarada equations). Presentation Slides

Friday, January 17 (8-11am) [Room 102, Colorado Convention Center]

Michael Filippakis (Multiple and nodal solutions for nonlinear equations with a nonhomogeneous differential operator and concave-convex term-nodal solutions for nonlinear problems). Presentation Slides
Alan Mullenix (Mixed finite element methods for a linearized multilayer shallow water model). Presentation Slides
Bruce A. Wade (Smoothing properties and dimensional splitting with exponential time differencing schemes for advection-diffusion-reaction systems). Presentation Slides
Brian Moore (Structure-preserving exponential integrators with applications for damped-driven NLS). Presentation Slides
JaEun Ku (Flux based finite element methods). Presentation Slides
Joshua Lee Padgett (A nonlinear splitting algorithm for preserving asymptotic features of stochastic singular differential equations). Presentation Slides

This special session information may also be found in its ResearchGate project.