The Landau-Lifshitz equation (LLE) governing the flow of magnetic spin in a ferromagnetic material is a PDE with a noncanonical Hamiltonian structure. In this paper we derive a number of new formulations of the LLE as a partial differential equation on a multisymplectic structure. Using this form we show that the standard central spatial discretization of the LLE gives a semi-discrete multisymp...

The linear shallow water equations on the sphere are discretized on a quasi-uniform, geodesic, icosahedral Voronoi-Delaunay grid with a C-grid variable arrangement and semi-implicit time discretization. A finite volume discretization is employed for the continuity equation in conservation law form, using as control volumes either the hexagonal/pentagonal or the dual triangular cells. A geostrop...

Chatter vibrations strongly limit productivity in milling. Due to the presence of rotating parts with asymmetric stiffness and stability enhancement strategies which act through a periodic variation stiffness, there is growing interest estimating maps systems Linear Time Periodic dynamics together cutting excitation. Applying Exponentially Modulated test signals dynamic force equation represent...

Integration factor methods are a class of ‘‘exactly linear part’’ time discretization methods. In [Q. Nie, Y.-T. Zhang, R. Zhao, Efficient semi-implicit schemes for stiff systems, Journal of Computational Physics, 214 (2006) 521–537], a class of efficient implicit integration factor (IIF) methods were developed for solving systems with both stiff linear and nonlinear terms, arising from spatial...

Abstract Modelling real processes often results in several suitable models. In order to be able distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., so-called T-optimal designs. These consist of the (design) points from generally continuous design space at models deviate most each other under condition that they are fitted those points. Thus, T-criter...

We present a Ritz-Galerkin discretization on sparse grids using pre-wavelets, which allows to solve elliptic differential equations with variable coefficients for dimension d = 2, 3 and higher dimensions d > 3. The method applies multilinear finite elements. We introduce an efficient algorithm for matrix vector multiplication using a Ritz-Galerkin discretization and semi-orthogonality. This alg...

We present a higher order accurate discontinuous Galerkin finite element method for the simulation of linear free-surface gravity waves. The method uses the classical Runge-Kutta method for the time discretization of the free-surface equations and the discontinuous Galerkin method for the space discretization. In order to circumvent numerical instabilities arising from an asymmetric mesh a stab...

We present a direct discretization of the electronic Schrödinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor product construction. We restrict these spaces to the case of antisymmetric functions. To obtain finite-dimensional subspaces we first discuss semi-discretization with respect ...