We study the spatial semidiscretizations obtained by applying Runge–Kutta (RK) and partitioned Runge–Kutta (PRK) methods to multisymplectic Hamiltonian partial differential equations. These methods can be regarded as multisymplectic hp-finite element methods for wave equations. All the methods we consider are multisymplectic; we determine their properties with regard to existence of solutions, ...

In this article, we study the problem of minimizing sum potentially nondifferentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication network is not coordinated. We behavior algorithm based on dual decomposition and block coordinate subgradient methods under assumptions weaker than those used literature. At same time, allow different a...