Equilibration based on classes Equilibrator and EquilibrationProblem

[brodbeck-m]

Equilibration shall be defined based on an abstract class 'Equilibrator'. This class (which has a c++ analogon) holds the basic information of the equilibartion process and the precompiled integration kernels for BCs and the (constrained) minimisation problem. This class is therefore mesh-independent. For a given mesh an EquilibrationProblem is created from this definitions, which contains the actual solution process.

Open issue 1: The equilibration routines currently generates ProblemData, KernelData and optionally quadrature kernels. Assuming a persistent EquilibrationProblem, these classes could be initialised once and kept, as long as the mesh is not changed or the EquilibrationProblem exists. Should that be changed.

Open issue 2: How should fluxes with discontinuous coefficients be handled, as these coefficient functions are required for the primal as well as the dual problem?

[brodbeck-m]

General outline of the class Equilibrator:

• [ ] Holds required, mesh independent forms for equilibration and the calculation of boundary conditions
• [ ] Variable for a physical time
• [ ] Update method for the time
• [ ] Setter method instantiating an EquilibrationProblem

[brodbeck-m]

General outline of the class EquilibrationProblem (Base class in section basic):

• [ ] List of functions for the H(div) conforming fluxes
• [ ] List of functions for the projected fluxes
• [ ] List of functions for the projected RHS
• [ ] Handle for the discontinous coefficients
• [ ] A function for the Korn constants
• [ ] Lists of Dirichlet facets of the primal problem
• [ ] Lists of flux BCs (each BC is a instance of FluxBC)
• [ ] Identifier if stresses are equilibrated
• [ ] Identifier if the problem has transient boundary conditions
• [ ] Variable of the physical time
• [ ] Update method for the physical time
• [ ] A solution method for the equilibration method

General outline of the class EquilibrationProblem (for the Ern and Vohralik strategy):

• [ ] Forms a and l of the constrained minimisation (constrained) minimisation problem

General outline of the class EquilibrationProblem (for the semi-explicit strategy):

• [ ] The KernelData
• [ ] The integration kernels for unconstrained flux and constrained stress minimisation