Advanced Numerical Studies in Nonlinear Partial Differential Equations
When computational issues related to partial differential equations are addressed it is typically from the applied mathematics perspective, and therefore in the setting of some intended application or future application. Rarely are the theoretical issues in PDEs themselves addressed using computational methodology. Given the vast increases in computing power being made available and the important role that such technology is playing in other sciences, it is natural to ask how high performance computing can be brought to bear in resolving fundamental questions about the structure, solvability, regularity, or asymptotic behavior of partial differential equations.
How much can be learned from numerics? It might be hard to build a rigorous proof around a computer simulation, but such simulations could provide insight or suggest directions for theoretical investigation. Of particular interest are no holds barred approaches which would involve really massive computational problems in order to provide such theoretical insight. The goal of this 4-day meeting, jointly organized by the Numerical Algorithms and Intelligent Software Centre and the Centre for Analysis and Nonlinear PDE, is to study problems at the interface of the two communities. This meeting will examine a variety of different problems in nonlinear partial differential equations for which numerical treatments and the use of high performance computers may lead to important new insight. Topics to be considered include:
- Hamiltonian PDEs, including examples such as the Euler equations and Nonlinear Schroedinger Equations
- Applications of such systems
- Integrability, regularity, ergodicity, and probabilistic issues and their interpretation using numerics
- Advances in numerical methods, such as symplectic and multisymplectic integrators
- High performance computing methods and there use in nonlinear PDE