In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of Nöther’s theorem from the formal variatio...

Higher order (p-version) finite element methods have been shown to be clearly superior to low order finite element methods when properly applied. However, the application of p-version finite elements for general 3-D geometries requires the careful construction and control of the mesh. A 2-D elasticity problem with curved boundary is used to clearly illustrate the influence of the mesh shape geo...

this paper introduces a new method for accelerating current sluggish fem and improving memory demand in fem problems with high node resolution or bulky structures. like most of the numerical methods, fem results to a matrix equation which normally has huge dimension. breaking the main matrix equation into several smaller size matrices, the solving procedure can be accelerated. for implementing ...

In linear thermoelasticity models, the temperature T and the displacement components u1, u2 exhibit large qualitative differences: While T typically is very smooth everywhere in the domain, the displacements u1, u2 have singular gradients (stresses) at re-entrant corners and edges. The mesh must be extremely fine in these areas so that stress intensity factors are resolved sufficiently. Among t...