Spectrally accurate space-time solution of Hamiltonian PDEs
For researchers solving Hamiltonian PDEs with stiff oscillations, this provides a more efficient spectral-in-time method.
The paper adapts Hamiltonian Boundary Value Methods (HBVMs) for stiffly-oscillatory Hamiltonian PDEs, achieving spectral accuracy in time for space semi-discretized problems. The new implementation improves efficiency over standard approaches.
Recently, the numerical solution of multi-frequency, highly-oscillatory Hamiltonian problems has been attacked by using Hamiltonian Boundary Value Methods (HBVMs) as spectral methods in time. When the problem derives from the space semi- discretization of (possibly Hamiltonian) partial differential equations (PDEs), the resulting problem may be stiffly-oscillatory, rather than highly-oscillatory. In such a case, a different implementation of the methods is needed, in order to gain the maximum efficiency.