DOLFINx_MPCindex-dokken2025mpc: Multi-point constraints framework for DOLFINx index-baratta2025dolfinx

`DOLFINx_MPC`[Dok25]: Multi-point constraints framework for DOLFINx [BDD+25]#

This library is an add-on to DOLFINx for imposing multi-point constraints, linear relations between degrees of freedom,

\[ u_s = \sum_j c_{sj}\, u_{m_j} + g_s, \]

where each constrained, slave, degree of freedom \(u_s\) is given by master degrees of freedom \(u_{m_j}\), with known coefficients \(c_{sj}\) and an offset \(g_s\). A master may carry a Dirichlet condition, and its value is then part of the offset. The constraints are eliminated from the system as it is assembled, so the solution satisfies them exactly.

Below you will find several examples of how to use the libary:

Spiders#

Joining two bodies with a rigid spider (RBE2)

Spreading a load over two bodies with a flexible spider (RBE3)

A double pendulum: two beams on two pins

Periodic conditions#

Anisotropic wave system with periodic boundary conditions

Periodic boundary conditions for a representative volume element

Periodic boundary conditions for a representative volume element: finite strain

Periodic boundary conditions for a three-dimensional representative volume element

Periodicity in one direction: a layer with an affine periodic part

Changing the coefficients of a multi-point constraint

Several spaces and meshes#

Mortar coupling: a Lagrange multiplier on a submesh

Mortar coupling of two subdomains

Bulk–surface coupling through a submesh

Integral constraints#

Fixing a mean value with an affine multi-point constraint

Prescribing a boundary average with an affine multi-point constraint

Prescribing a flow rate with an affine multi-point constraint

Slip conditions#

Stokes flow with slip conditions

Stokes problem with slip condition using NEST matrices

References#

[BDD+25]

Igor A. Baratta, Joseph P. Dean, Jørgen S. Dokken, Michal Habera, Jack S. Hale, Chris N. Richardson, Marie E. Rognes, Matthew W. Scroggs, Nathan Sime, and Garth N. Wells. Dolfinx: the next generation fenics problem solving environment. December 2025. doi:10.5281/zenodo.18101307.

[Dok25]

Jørgen Schartum Dokken. DOLFINx-MPC. July 2025.